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Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume contains 6th Standard Go Math solutions which will make students understand the concepts easily help the students to score well in the exams. This Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume. And in this, each and every question was explained intimately. The answers in this chapter are explained in a simple way that anyone can understand easily.
This chapter 11 contains Three-Dimensional Figures and Nets, Explore Surface Area Using Nets, Surface Area of Prisms, etc. are explained clearly which makes the scholars learn quickly. Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume. questions are explained in a basic way that students will never feel any difficulty in learning. By this, students can gain good knowledge and this is helpful in finish student's assignments also.
Lesson 1: Three-Dimensional Figures and Nets
Share and Show – Page No. 599
Problem Solving + Applications – Page No. 600
Three-Dimensional Figures and Nets – Page No. 601
Lesson Check – Page No. 602
Lesson 2: Investigate • Explore Surface Area Using Nets
What's the Error? – Page No. 606
Explore Surface Area Using Nets – Page No. 607
Lesson 3: Algebra • Surface Area of Prisms
Unlock the Problem – Page No. 612
Surface Area of Prisms – Page No. 613
Lesson 4: Algebra • Surface Area of Pyramids
Surface Area of Pyramids – Page No. 619
Mid-Chapter Checkpoint – Vocabulary – Page No. 621
Page No. 622
Lesson 5: Investigate • Fractions and Volume
Fractions and Volume – Page No. 627
Lesson 6: Algebra • Volume of Rectangular Prisms
Aquariums – Page No. 632
Volume of Rectangular Prisms – Page No. 633
Lesson 7: Problem Solving • Geometric Measurements
On Your Own – Page No. 638
Problem Solving Geometric Measurements – Page No. 639
Chapter 11 Review/Test
Chapter 11 Review/Test – Page No. 641
Identify and draw a net for the solid figure.
Answer: The base Square or Rectangle, and lateral faces are Triangle and the figure is a Square pyramid or Rectangular pyramid.
Answer: Cube or Rectangular prism.
Explanation: The base is a square or rectangle and lateral faces are squares are rectangle. The figure is a Cube or Rectangular prism.
Identify and sketch the solid figure that could be formed by the net.
Answer: Triangular pyramid.
Explanation: The net has four triangles, so it is a triangular pyramid.
Answer: Cube
Explanation: The net has six squares.
Answer: Triangular prism.
Explanation: The base is a rectangle and the lateral faces are triangle and rectangles, so it is a triangular prism.
Answer: Rectangular Prism.
Explanation: The base is a rectangle and the lateral faces are squares and rectangles. And it is a Rectangular prism.
The lateral faces and bases of crystals of the mineral galena are congruent squares. Identify the shape of a galena crystal.
Explanation: The shape of the galena is Cube.
Rhianon draws the net below and labels each square. Can Rhianon fold her net into a cube that has letters A through G on its faces? Explain.
Answer: No, she cannot fold her net into a cube. Rhianon's net has seven squares but there are only six squares in a net of a cube.
Describe A diamond crystal is shown. Describe the figure in terms of the solid figures you have seen in this lesson.
Answer: We can see that Diamond crystal consists of two square pyramids with congruent bases and the pyramids are reversed and placed base to base.
Sasha makes a triangular prism from paper.
The bases are _____.
The lateral faces are _____.
The bases are Triangle
The lateral faces are Rectangle
Answer: Rectangular Prism
Answer: Cube, Rectangular prism
Answer: Square Pyramid
Answer: Triangular Prism
Hobie's Candies are sold in triangular-pyramidshaped boxes. How many triangles are needed to make one box?
Explanation: As triangled pyramids have four faces.
Nina used plastic rectangles to make 6 rectangular prisms. How many rectangles did she use?
Describe how you could draw more than one net to represent the same three-dimensional figure. Give examples.
How many vertices does a square pyramid have?
Each box of Fred's Fudge is constructed from 2 triangles and 3 rectangles. What is the shape of each box?
Bryan jogged the same distance each day for 7 days. He ran a total of 22.4 miles. The equation 7d = 22.4 can be used to find the distance d in miles he jogged each day. How far did Bryan jog each day?
Answer: 3.2 miles
Explanation: As given equation 7d= 22.4,
d= 22.4÷7
= 3.2 miles.
A hot-air balloon is at an altitude of 240 feet. The balloon descends 30 feet per minute. What equation gives the altitude y, in feet, of the hot-air balloon after x minutes?
Answer: Y= 240- 30X.
Explanation: Given altitude Y, and the ballon was descended 30 feet per minute. So the equation is Y= 240- 30X.
A regular heptagon has sides measuring 26 mm and is divided into 7 congruent triangles. Each triangle has a height of 27 mm. What is the area of the heptagon?
Answer: 351 mm2
Explanation: Area of heptagon= 1/2 b×h
= 1/2 (26)×(27)
= 13×27
= 351 mm2
Alexis draws quadrilateral STUV with vertices S(1, 3), T(2, 2), U(2, –3), and V(1, –2). What name best classifies the quadrilateral?
Answer: Parallelogram
Use the net to find the surface area of the prism.
Explanation: First we must find the area of each face
A= 4×3= 12
B= 4×3= 12
C= 5×4= 20
D= 5×4= 20
E= 5×3= 15
F= 5×3= 15
So, the surface area is 12+12+20+20+15+15= 94 cm2
Answer: 222 cm2
Explanation: Area of a rectangular prism is 2(wl+hl+hw) = 2(7×9+ 3×9+ 3×7)
= 2(63+27+21)
= 2(111)
= 222 cm2
Explanation: Area of a rectangular prism is 2(wl+hl+hw) = 2(10×10+ 10×10+ 10×10)
= 2(100+100+100)
Explanation: Area of a rectangular prism is 2(wl+hl+hw) = 2(15×5+ 5×5+ 15×5)
Problem Solving + Applications
A cereal box is shaped like a rectangular prism. The box is 20 cm long by 5 cm wide by 30 cm high. What is the surface area of the cereal box?
Answer: 1700 cm2
Explanation: The length of the box is 20 cm, the wide is 5 cm and the height is 30 cm. So surface area of the cereal box is 2(wl+hl+hw)= 2(20×5+30×20+30×5)
= 1700 cm2
Darren is painting a wooden block as part of his art project. The block is a rectangular prism that is 12 cm long by 9 cm wide by 5 cm high. Describe the rectangles that make up the net for the prism.
In Exercise 6, what is the surface area, in square meters, that Darren has to paint?
Explanation: Surface area = 2(wl+hl+hw)
= 2(9×12+5×12+ 5×9)
= 2(108+60+45)
Emilio is designing the packaging for a new MP3 player. The box for the MP3 player is 5 cm by 3 cm by 2 cm. Emilio needs to find the surface area of the box.
Look at how Emilio solved the problem. Find his error.
STEP 1: Draw a net.
STEP 2: Find the areas of all the faces and add them.
Face A: 3 × 2 = 6 cm2.
Face B: 3 × 5 = 15 cm2.
Face C: 3 × 2 = 6 cm2.
Face D: 3 × 5 = 15 cm2.
Face E: 3 × 5 = 15 cm2.
Face F: 3 × 5 = 15 cm2.
The surface area is 6 + 15 + 6 + 15 + 15 + 15 = 72 cm2.
Correct the error. Find the surface area of the prism.
Answer: Emilio drew the net incorrectly Face D and F should have been 2 cm by 5 cm, not 3 cm by 5 cm
Face A: 3×2= 6 cm2
Face B: 3×5= 15 cm2
Face C: 3×2= 6 cm2
Face D: 2×5= 10 cm2
Face E: 3×5= 15 cm2
Face F: 2×5= 10 cm2
So, the surface area of the prism area is 6+15+6+10+15+10= 62 cm2.
For numbers 9a–9d, select True or False for each statement.
9a. The area of face A is 10 cm2.
9b. The area of face B is 10 cm2.
9c. The area of face C is 40 cm2.
9d. The surface area of the prism is 66 cm2.
Explanation: The area of face A is 2×5= 10 cm2.
Explanation: The area of face B is 2×8= 16 cm2.
Answer: The area of face C is 8×5= 40 cm2.
Answer: 160 cm2.
Explanation: The surface area of the prism is
= 2×10+2×10+2×40
= 20+20+80
= 160 cm2.
Use the net to find the surface area of the rectangular prism.
_______ square units
Answer: 52 square units.
The area of face A is 6 squares.
The area of face B is 8 squares.
The area of face C is 6 squares.
The area of face D is 12 squares.
The area of face E is 8 squares.
The area of face F is 12 squares.
The surface area is 6+8+6+12+8+12= 52 square units.
Answer: 112 square units.
The area of face A is 16 squares.
The area of face C is 32 squares.
The area of face E is 32 squares.
The area of face F is 8 squares.
The surface area is 112 square units.
Explanation: Area= 2(wl+hl+hw)
= 2(3×7+3×7+3×3)
= 2(21+21+9)
= 2(51)
_______ in.2
Answer: 58 in.2
= 2(5×1+ 4×1+ 4×5)
= 2(5+4+20)
= 58 in.2
_______ ft2
Answer: 77 ft2
= 2(6.5×2+3×2+3×6.5)
= 2(13+6+19.5)
= 2(38.5)
= 77 ft2
Jeremiah is covering a cereal box with fabric for a school project. If the box is 6 inches long by 2 inches wide by 14 inches high, how much surface area does Jeremiah have to cover?
Answer: 248 in.2
Explanation: Surface area of a cereal box is 2(wl+hl+hw)
= 2(2×6+14×6+14×2)
= 248 in.2
Tia is making a case for her calculator. It is a rectangular prism that will be 3.5 inches long by 1 inch wide by 10 inches high. How much material (surface area) will she need to make the case?
Explanation: Surface Area= 2(wl+hl+hw)
= 2(1×3.5+ 10×3.5+ 10×1)
= 2(3.5+35+10)
Explain in your own words how to find the surface area of a rectangular prism.
Answer: To find the surface area we must know the width, length, and height of the prism and then we can apply the formula which is
Surface area= 2(width ×length)+ 2(length×height)+ 2(height×width)
= 2(width ×length+ length×height+ 2(height×width)
Gabriela drew a net of a rectangular prism on centimeter grid paper. If the prism is 7 cm long by 10 cm wide by 8 cm high, how many grid squares does the net cover?
_______ cm2
Explanation: Surface area is 2(wl+hl+hw)
= 2(10×7+8×7+8×10)
Ben bought a cell phone that came in a box shaped like a rectangular prism. The box is 5 inches long by 3 inches wide by 2 inches high. What is the surface area of the box?
Katrin wrote the inequality x + 56 < 533. What is the solution of the inequality?
Answer: X<477.
Explanation: X+56<533
= X<533-56
= X<477.
The table shows the number of mixed CDs y that Jason makes in x hours.
Which equation describes the pattern in the table?
Answer: y= 5x
y/x = 10/2= 15/4= 3
y= 5x
The pattern is y is x multipled by 5.
A square measuring 9 inches by 9 inches is cut from a corner of a square measuring 15 inches by 15 inches. What is the area of the L-shaped figure that is formed?
Explanation: The area of a square A= a2, so we will find the area of each square.
Area= 92
= 9×9
And the area of another square is
A= 152
So the area of L shaped figure is 225-81= 144 in.2
Boxes of Clancy's Energy Bars are rectangular prisms. How many lateral faces does each box have?
Explanation: As Lateral faces are not included in the bases, so rectangular prism has 4.
Use a net to find the surface area.
Explanation: The area of each face is 2 ft×2 ft= 4 ft and the number of faces is 6, so surface area is 6×4= 24 ft2
The area of face A is 16×6= 96 cm2
The area of face B is 16×8= 128 cm2
The area of face C and D is 1/2 × 6×8= 24 cm2
The area of face E is 16×10= 160 cm2
The surface 96+128+2×24+160= 432 cm2
Answer: 155.5 in.2
The area of face A and E is 8 ½ × 3½
= 17/2 × 7/2
= 119/4
= 29.75 in.2
The area of face B and F is 8 ½×4
= 17 ½ × 4
The area of face C and D is 3 ½×4
7/2 × 4= 14 in.2
The surface area is 2×29.75+2×34+2×14
= 59.5+68+28
= 155.5 in.2
_______ m2
The area of face A and E is 8×3= 24 m2
The area of face B and F is 8×5= 40 m2
The area of face C and D is 3×5= 15 m2
The surface area is 2×24+2×40+2×15
= 158 m2
_______ \(\frac{□}{□}\) in.2
The area of each face is 7 1/2 × 7 1/2
= 15/2 × 15/2
= 225/4 in.2
The no.of faces are 6 and the surface area is 6× 225/4
= 337 1/2 in.2
Attend to Precision Calculate the surface area of the cube in Exercise 5 using the formula S = 6s2. Show your work.
Answer: 337 1/2 in.2
Explanation: As S= s2
= 6(7 1/2)2
= 6(15/2)2
= 6(225/4)
The Vehicle Assembly Building at Kennedy Space Center is a rectangular prism. It is 218 m long, 158 m wide, and 160 m tall. There are four 139 m tall doors in the building, averaging 29 m in width. What is the building's outside surface area when the doors are open?
a. Draw each face of the building, not including the floor.
b. What are the dimensions of the 4 walls?
Answer: The 2 walls measure 218 m ×160 m and 2 walls measure by 158 m×160 m.
c. What are the dimensions of the roof?
Answer: The dimensions of the roof are 218 m×158 m.
d. Find the building's surface area (not including the floor) when the doors are closed.
Answer: 1,54,764 m2
The area of two walls is 218×160= 34,880 m2
The area of the other two walls is 158×160= 25,280 m2
The area of the roof 158×218= 34,444 m2
The surface area is 2× 34,880+ 2× 25,280+ 34,444
= 69,760+ 50,560+ 34,444
= 1,54,764 m2
e. Find the area of the four doors.
Answer: 16,124 m2
Explanation: Area of a door is 139×29 = 4031 m2
And the area of 4 doors is 4×4031= 16,124 m2
f. Find the building's surface area (not including the floor) when the doors are open.
Explanation: The building's surface area (not including the floor) when the doors are open is
1,54,764 – 16,124= 1,38,640 m2
A rectangular prism is 1 \(\frac{1}{2}\) ft long, \(\frac{2}{3}\) ft wide, and \(\frac{5}{6}\) ft high. What is the surface area of the prism in square inches?
Explanation: The area of two faces is 1 1/2× 5/6
= 3/2 × 5/6
= 5/4 cm2
The area of two faces is 2/3 × 5/6
= 5/9 ft2
The area of two faces is 1 1/2× 2/3
= 1 ft2
The surface area of the prism is 2(wl+hl+hw)
= 2(5/4 + 5/9 + 1)
= 2( 1.25+0.55+1)
= 2.5+1.1+2
= 5.61 ft2
As 1 square foot = 144 square inches
so 5.61×144 = 807.84
A gift box is a rectangular prism. The box measures 8 inches by 10 inches by 3 inches. What is its surface area?
The area of face A and Face E is 8×10= 80 in.2
The area of face B and Face F is 8×3= 24 in.2
The area of face C and Face D is 10×3= 30 in.2
= 160+48+60
Answer: 486 ft2
= 486 ft2
Explanation: Area = 1/2 bh
= 1/2 (6)(8)
As there are 2 triangles, so 2×24= 48.
Surface Area= (wl+hl+hw)
= (6×12+8×12+12×10)
Total Surface area = 228+48
A shoe box measures 15 in. by 7 in. by 4 \(\frac{1}{2}\) in. What is the surface area of the box?
The area of two faces is 15×7= 105 in.2
The area of two faces is 15× 4 1/2
= 15 × 9/2
= 15 × 4.5
= 67.5 in.2
The area of two faces is 7× 4 1/2
= 7× 9/2
= 7× 4.5
The surface area is 2×105+ 2×67.5+ 2×31.5
= 210+ 135+ 63
Vivian is working with a styrofoam cube for art class. The length of one side is 5 inches. How much surface area does Vivian have to work with?
The area of each face is 5×5= 25 in.2
The number of faces that styrofoam cube has is 6
So the surface area is 6×25= 150 in.2
Explain why a two-dimensional net is useful for finding the surface area of a three-dimensional figure.
Answer: Two-dimensional net is useful because by using a two-dimensional net you can calculate the surface area of each face and add them up to find the surface area of the three-dimensional figure.
What is the surface area of a cubic box that contains a baseball that has a diameter of 3 inches?
The area of each face is 3×3= 9 in.2
The number of faces for a cubic box is 6 in.2
The surface area of box that contains a baseball is 6×9= 54 in.2
A piece of wood used for construction is 2 inches by 4 inches by 24 inches. What is the surface area of the wood?
The area of two faces is 4×2= 8 in.2
The area of two faces is 2×24= 48 in.2
The area of two faces is 24×4= 96 in.2
So the surface area is 2×8+ 2×48+ 2×96
= 16+96+192
Detergent costs $4 per box. Kendra graphs the equation that gives the cost y of buying x boxes of detergent. What is the equation?
Answer: Y= 4X.
Explanation: The total price Y and the price is equal to 4 × X, and X is the number of boxes that Kendra buys. So the equation is Y=4X.
A trapezoid with bases that measure 8 inches and 11 inches has a height of 3 inches. What is the area of the trapezoid?
Answer: 28.5 in.2
Area of a trapezoid is 1/2(b1+b2)h
= 1/2(8+11)3
= 1/2(19)3
= 1/2 (57)
City Park is a right triangle with a base of 40 yd and a height of 25 yd. On a map, the park has a base of 40 in. and a height of 25 in. What is the ratio of the area of the triangle on the map to the area of City Park?
Answer: 1296:1.
Area= 1/2 bh
= 1/2 (40)(25)
= (20)(25)
= 500 yd2
So area of city park is 500 yd2
= 500 in2
So area on the map is 500 in
as 1 yd2= 1296 in2
So 500 in2 = 500×1296
So, the ratio of the area of the triangle on the map to the area of City Park is 648,000:500
= 1296:1.
What is the surface area of the prism shown by the net?
The area of two faces is 18 squares
The area of two faces is 6 squares
So the surface area is 2×18+ 2×6+ 2×12
= 72 square units.
Use a net to find the surface area of the square pyramid.
Area of the base 5×5= 25 ,
and area of one face is 1/2 × 5 × 8
= 5× 4
= 20 cm2
The surface area of a pyramid is 25+ 4×20
= 25+80
A triangular pyramid has a base with an area of 43 cm2 and lateral faces with bases of 10 cm and heights of 8.6 cm. What is the surface area of the pyramid?
The area of one face is 1/2×10×8.6
= 5×8.6
The surface area of the pyramid is 43+3×43
= 43+ 129
A square pyramid has a base with a side length of 3 ft and lateral faces with heights of 2 ft. What is the lateral area of the pyramid?
The area of one face is 1/2×3×2= 3 ft2
The lateral area of the pyramid is 4×3= 12 ft2
The area of the base is 8×8= 64
The area of one face is 1/2 ×8×9
= 64+144
The area of base is 10×10= 100
The area of one place is 1/2×10×6
= 10×3
The surface area of the pyramid is 100+4×30
= 100+120
The area of one face is 1/2×8×12.5
= 4×12.5
The surface area of the pyramid is 64+ 4×50
The Pyramid Arena is located in Memphis, Tennessee. It is in the shape of a square pyramid, and the lateral faces are made almost completely of glass. The base has a side length of about 600 ft and the lateral faces have a height of about 440 ft. What is the total area of the glass in the Pyramid Arena?
Answer: 5,28,000 ft2
The area of one face is 1/2×600×440= 1,32,000 ft2
The surface of tha lateral faces is 4× 1,32,000= 5,28,000 ft2
So, the total area of the glass in the arena is 5,28,000 ft2
Use the table for 8–9.
The Great Pyramids are located near Cairo, Egypt. They are all square pyramids, and their dimensions are shown in the table. What is the lateral area of the Pyramid of Cheops?
The area of one face is 1/2×230×180
= 230×90
= 20,700 m2
The lateral area of the pyramid of Cheops is 4×20,700= 82,800 m2
What is the difference between the surface areas of the Pyramid of Khafre and the Pyramid of Menkaure?
The area of the base is 215×215= 46,225
= 215× 87
The surface area of Pyramid Khafre is= 46,225+4×18,705
= 46,225+ 74820
= 121,045 m2
The area of the base 103×103= 10,609
The area of one face is 1/2×103×83
= 8549÷2
= 4274.4 m2
The surface area of the Pyramid of Menkaure is 10,609+4×4274.5
= 10,609+ 17,098
The difference between the surface areas of the Pyramid of Khafre and the Pyramid of Menkaure
= 121,405-27,707
Write an expression for the surface area of the square pyramid shown.
Answer: 6x+9 ft2.
Explanation: The expression for the surface area of the square pyramid is 6x+9 ft2.
Make Arguments A square pyramid has a base with a side length of 4 cm and triangular faces with a height of 7 cm. Esther calculated the surface area as (4 × 4) + 4(4 × 7) = 128 cm2. Explain Esther's error and find the correct surface area
Answer: 72 cm2.
Explanation: Esther didn't apply the formula correctly, she forgot to include 1/2 in the calculated surface area.
The correct surface area is (4×4)+4(1/2 ×4×7)
= 16+4(14)
= 72 cm2.
Jose says the lateral area of the square pyramid is 260 in.2. Do you agree or disagree with Jose? Use numbers and words to support your answer.
Explanation: No, I disagree with Jose as he found surface area instead of the lateral area, so the lateral area is
4×1/2×10×8
= 2×10×8
_______ mm2
Answer: 95 mm2
The area of the base is 5×5= 25 mm2
The area of one face is 1/2×5×7
= 35/2
= 17.5 mm2
The surface area is 25+4×17.5
= 25+4×17.5
= 95 mm2
The area of the base is 18×18= 324 cm2
The area of one face is 1/2×18×8
The surface area is 324+4×72
_______ yd2
Answer: 51.25 yd2
The area of the base is 2.5×2.5= 6.25 mm2
The area of one face is 1/2×2.5×9
= 22.5/2
= 11.25 yd2
= 6.25+4×11.25
= 6.25+45
Answer: 180 in2
The area of the base is 10×10= 100 in2
The area of one face is 1/2×4×10
= 2×10
= 20 in2
= 100+4×20
= 100+80
Cho is building a sandcastle in the shape of a triangular pyramid. The area of the base is 7 square feet. Each side of the base has a length of 4 feet and the height of each face is 2 feet. What is the surface area of the pyramid?
The surface area of the triangular pyramid is 7+3×4
= 7+12
The top of a skyscraper is shaped like a square pyramid. Each side of the base has a length of 60 meters and the height of each triangle is 20 meters. What is the lateral area of the pyramid?
Answer: 2400 m2
The area of the one face is 1/2×60×20
The lateral area of the pyramid is 4×600= 2400 m2
Write and solve a problem finding the lateral area of an object shaped like a square pyramid.
Answer: Mary has a triangular pyramid with a base of 10cm and a height of 15cm. What is the lateral area of the pyramid?
The area of one face is 1/2×10×15
The lateral area of the triangular pyramid is 3×75
A square pyramid has a base with a side length of 12 in. Each face has a height of 7 in. What is the surface area of the pyramid?
The area of the base is 12×12= 144 in.2
The surface area of the square pyramid is 144+4×42
= 144+ 168
The faces of a triangular pyramid have a base of 5 cm and a height of 11 cm. What is the lateral area of the pyramid?
Answer: 82.5 cm2
= 27.5 cm2
The lateral area of the triangular pyramid is 3×27.5= 82.5 cm2
What is the linear equation represented by the graph?
Answer: y=x+1.
Explanation: As the figure represents that every y value is 1 more than the corresponding x value, so the linear equation is y=x+1.
A regular octagon has sides measuring about 4 cm. If the octagon is divided into 8 congruent triangles, each has a height of 5 cm. What is the area of the octagon?
Area is 1/2bh
= 1/2× 4×5
So the area of each triangle is 10 cm2
and the area of the octagon is 8×10= 80 cm2
Carly draws quadrilateral JKLM with vertices J(−3, 3), K(3, 3), L(2, −1), and M(−2, −1). What is the best way to classify the quadrilateral?
Answer: It is a Trapezoid.
Explanation: It is a Trapezoid.
A rectangular prism has the dimensions 8 feet by 3 feet by 5 feet. What is the surface area of the prism?
The area of the two faces of the rectangular prism is 8×3= 24 ft2
The surface area of the rectangular prism is 2×24+2×40+2×15
Choose the best term from the box to complete the sentence.
_____ is the sum of the areas of all the faces, or surfaces, of a solid figure.
Answer: Surface area is the sum of the areas of all the faces, or surfaces, of a solid figure.
A three-dimensional figure having length, width, and height is called a(n) _____.
Answer: A three-dimensional figure having length, width, and height is called a(n) solid figure.
The _____ of a solid figure is the sum of the areas of its lateral faces.
Answer: The lateral area of a solid figure is the sum of the areas of its lateral faces.
Use a net to find the lateral area of the square pyramid.
The lateral area of the square pyramid is 4×54= 216 in.2
Use a net to find the surface area of the prism.
The area of face A and E is 10×5= 50 cm2
The area of face B and F is 10×7= 70 cm2
The area of face C and D is 7×5= 35 cm2
The surface area of the prism is 2×50+2×70+2×35
= 100+140+70
A machine cuts nets from flat pieces of cardboard. The nets can be folded into triangular pyramids used as pieces in a board game. What shapes appear in the net? How many of each shape are there?
Answer: 4 triangles.
Explanation: There are 4 triangles.
Fran's filing cabinet is 6 feet tall, 1 \(\frac{1}{3}\) feet wide, and 3 feet deep. She plans to paint all sides except the bottom of the cabinet. Find the area of the sides she intends to paint.
The two lateral face area is 6×1 1/3
The area of the other two lateral faces is 6×3= 18
The area of the top and bottom is 3× 1 1/3
The area of the sides she intends to paint is 2×8+2×18+4
= 16+36+4
A triangular pyramid has lateral faces with bases of 6 meters and heights of 9 meters. The area of the base of the pyramid is 15.6 square meters. What is the surface area of the pyramid?
Answer: 96.6 m2
The area of one face is 1/2× 6× 9
= 27 m2
The surface area of the triangular pyramid is 15.6+3×27
= 15.6+ 81
= 96.6 m2
What is the surface area of a storage box that measures 15 centimeters by 12 centimeters by 10 centimeters?
The area of two faces is 15×12= 180 cm2
The area of another two faces is 15×10= 150 cm2
The area of the other two faces is 10×12= 120 cm2
So surface area of the storage box is 2×180+2×150+2×120 cm2
= 360+300+240
A small refrigerator is a cube with a side length of 16 inches. Use the formula S = 6s2 to find the surface area of the cube.
Answer: 1,536 in.2
Area = s2
= 6×(16)2
= 6× 256
= 1,536 in.2
A prism is filled with 38 cubes with a side length of \(\frac{1}{2}\) unit. What is the volume of the prism in cubic units?
_______ \(\frac{□}{□}\) cubic units
Answer: 4.75 cubic units
The volume of the cube is S3
The volume of a cube with S= (1/2)3
= 1/2×1/2×1/2
= 1/8
= 0.125 cubic units
As there are 38 cubes so 38×0.125= 4.75 cubic units.
Answer: 7.25 cubic units.
Find the volume of the rectangular prism.
_______ cubic units
Answer: 33 cubic units.
The volume of the rectangular prism is= Width×Height×Length
= 5 1/2 ×3×2
= 11/2 ×3×2
= 33 cubic units.
Answer: 91 1/8 cubic units.
= 4 1/2 ×4 1/2×4 1/2
= 9/2 ×9/2×9/2
= 91 1/8 cubic units.
Theodore wants to put three flowering plants in his window box. The window box is shaped like a rectangular prism that is 30.5 in. long, 6 in. wide, and 6 in. deep. The three plants need a total of 1,200 in.3 of potting soil to grow well. Is the box large enough? Explain.
Answer: No, the box is not large enough as the three plants need a total of 1,200 in.3 and here volume is 1,098 in.3
Volume= Width×Height×Length
= 30.5×6×6
Explain how use the formula V = l × w × h to verify that a cube with a side length of \(\frac{1}{2}\) unit has a volume of \(\frac{1}{8}\) of a cubic unit.
Answer: 1/8 cubic units
As length, width and height is 1/2′ so
Volume = Width×Height×Length
= 1/2 × 1/2 × 1/2
= 1/8 cubic units
Use the diagram for 7–10.
Karyn is using a set of building blocks shaped like rectangular prisms to make a model. The three types of blocks she has are shown at right. What is the volume of an A block? (Do not include the pegs on top.)
\(\frac{□}{□}\) cubic units
Explanation: Volume = Width×Height×Length
= 1× 1/2 ×1
How many A blocks would you need to take up the same amount of space as a C block?
_______ A blocks
Answer: No of blocks required to take up the same amount of space as a C block is 4 A blocks.
= 1×2×1
= 2 cubic unit
No of blocks required to take up the same amount of space as a C block is 1/2 ÷2
= 4 A blocks
Karyn puts a B block, two C blocks, and three A blocks together. What is the total volume of these blocks?
Answer: 6 1/2 cubic units
Explanation: The volume of A block is
= 1×1 ×1/2
= 1/2 cubic units.
As Karyn puts three A blocks together, so 3× 1/2= 3/2 cubic units.
The volume of B block is
= 1×1 × 1
= 1 cubic units.
As Karyn puts only one B, so 1 cubic unit.
The volume of C block is
As Karyn puts two C blocks together, so 2× 2= 4 cubic units.
So, the total volume of these blocks is 3/2 + 1+ 4
= 3/2+5
= 6 1/2 cubic units
Karyn uses the blocks to make a prism that is 2 units long, 3 units wide, and 1 \(\frac{1}{2}\) units high. The prism is made of two C blocks, two B blocks, and some A blocks. What is the total volume of A blocks used?
Answer: 3 cubic units.
= 2×3×1 1/2
= 2×3× 3/2
The total volume of A block used is 9-(2×2)-(2×1)
= 9- 4- 2
= 9-6
Verify the Reasoning of Others Jo says that you can use V = l × w × h or V = h × w × l to find the volume of a rectangular prism. Does Jo's statement make sense? Explain.
Explanation: Yes, Jo's statement makes sense because by the commutative property we can change the order of the variables of length, width, height and both will produce the same result.
A box measures 5 units by 3 units by 2 \(\frac{1}{2}\) units. For numbers 12a–12b, select True or False for the statement.
12a. The greatest number of cubes with a side length of \(\frac{1}{2}\) unit that can be packed inside the box is 300.
12b. The volume of the box is 37 \(\frac{1}{2}\) cubic units.
12a. __________
12b. __________
12a True.
12b True.
Explanation: The volume of the cube is S3
As there are 300 cubes so 300× 1/8= 75/2
= 3× 1 1/2× 1 1/2
= 3× 3/2 × 3/2
Answer: 22 1/2 cubic units
= 5×1× 4 1/2
= 22 1/2 cubic units
= 5 1/2× 1 1/2× 2
= 11/2×3/2×2
= 2 1/2× 2 1/2 × 4 1/2
Miguel is pouring liquid into a container that is 4 \(\frac{1}{2}\) inches long by 3 \(\frac{1}{2}\) inches wide by 2 inches high. How many cubic inches of liquid will fit in the container?
= 4 1/2 × 3 1/2 ×2
= 9/2 × 7/2 × 2
A shipping crate is shaped like a rectangular prism. It is 5 \(\frac{1}{2}\) feet long by 3 feet wide by 3 feet high. What is the volume of the crate?
_______ \(\frac{□}{□}\) ft3
Answer: 49 1/2 ft3
= 5 1/2 × 3 × 3
= 11/2 ×9
= 49 1/2 ft3
How many cubes with a side length of \(\frac{1}{4}\) unit would it take to make a unit cube? Explain how you determined your answer.
Answer: There will be 4×4×4= 64 cubes and 1/4 unit in the unit cube.
As the unit cube has a 1 unit length, 1 unit wide, and 1 unit height
So length 4 cubes = 4× 1/4= 1 unit
width 4 cubes = 4× 1/4= 1 unit
height 4 cubes = 4× 1/4= 1 unit
So there will be 4×4×4= 64 cubes and 1/4 unit in the unit cube.
A rectangular prism is 4 units by 2 \(\frac{1}{2}\) units by 1 \(\frac{1}{2}\) units. How many cubes with a side length of \(\frac{1}{2}\) unit will completely fill the prism?
Answer: 120 cubes
No of cubes with a side length of 1/2 unit is
Length 8 cubes= 8× 1/2= 4 units
Width 5 cubes= 5× 1/2= 5/2= 2 1/2 units
Height 3 cubes= 3× 1/2= 3/2= 1 1/2 units
So there are 8×5×3= 120 cubes in the prism.
A rectangular prism is filled with 196 cubes with \(\frac{1}{2}\)-unit side lengths. What is the volume of the prism in cubic units?
Explanation: As it takes 8 cubes with a side length of 1/2 to form a unit cube, so the volume of the prism in the cubic units is 196÷8= 24 1/2 cubic units.
A parallelogram-shaped piece of stained glass has a base measuring 2 \(\frac{1}{2}\) inches and a height of 1 \(\frac{1}{4}\) inches. What is the area of the piece of stained glass?
Answer: 3 1/8 in.2
Explanation: Area of a parallelogram = base×height
= 2 1/2 × 1 1/4
= 3 1/8 in.2
A flag for the sports club is a rectangle measuring 20 inches by 32 inches. Within the rectangle is a yellow square with a side length of 6 inches. What is the area of the flag that is not part of the yellow square?
Explanation: Area of a flag= Length×width
Area of the yellow square= S2
So the area of the flag that is not a part of the yellow square is 640-36= 604 in.2
What is the surface area of the rectangular prism shown by the net?
Answer: 80 square units
Area of two faces is 12 squares
Area of other two faces is 16 squares
Area of another two faces is 12 squares
So the surface area is 2×12+2×16+2×12
= 80 square units
What is the surface area of the square pyramid?
Explanation: The area of the base is 7×7= 49 cm2
And the area of one face is 1/2 × 7× 8
The surface area of the square pyramid is 49+4×28
Find the volume.
Answer: 3,937 1/2 in.3
Explanation: Volume= Length× wide× heght
= 10 1/2 ×15 × 25
= 11/2 × 15 × 25
= 4,125/2
= 3,937 1/2 in.3
Answer: 27/512 in.3
Explanation: Volume= Length× wide× height
=3/8 ×3/8 × 3/8
= 27/512 in.3
Find the volume of the prism.
Answer: 690 5/8in.3
= 8 1/2 × 6 1/2 × 12 1/2
= 17/2 × 13/2× 25/2
= 5525/2
= 690 5/8in.3
Answer: 125/4096 in.3
= 5/16 ×5/16 × 5/16
= 125/4096 in.3
Answer: 20 yd3
Area= 3 1/3 yd2
So Area= wide×height
3 1/3= w × 1 1/3
10/3= w× 4/3
w= 10/3 × 3/4
w= 5/2
w= 2.5 yd
Volume= Length×width×height
= 6× 2.5× 1 1/3
= 6×2.5× 4/3
= 2×2.5×4
= 20 yd3
Wayne's gym locker is a rectangular prism with a width and height of 14 \(\frac{1}{2}\) inches. The length is 8 inches greater than the width. What is the volume of the locker?
Explanation: As length is 8 inches greater than width, so 14 1/2+ 8
= 29/2+8
= 22 1/2 in
Then volume= Length×width×height
= 22 1/2 × 14 1/2 × 14 1/2
= 45/2× 29/2× 29/2
= 37845/8
Abraham has a toy box that is in the shape of a rectangular prism.
The volume is _____.
Explanation: Volume of rectangular prism is= Length×width×height
= 9/2 × 5/2× 3
Large public aquariums like the Tennessee Aquarium in Chattanooga have a wide variety of freshwater and saltwater fish species from around the world. The fish are kept in tanks of various sizes.
The table shows information about several tanks in the aquarium. Each tank is a rectangular prism.
Find the length of Tank 1.
V = l w h
52,500 = l × 30 × 35
\(\frac{52,500}{1,050}\) = l
50 = l
So, the length of Tank 1 is 50 cm.
Find the width of Tank 2 and the height of Tank 3.
Answer: Width of Tank 2= 8m, Height of the Tank 3= 10 m
The volume of Tank 2= 384 m3
so V= LWH
384= 12×W×4
W= 384/48
W= 8 m
So the width of Tank 2= 8m
The volume of Tank 3= 2160 m
2160= 18×12×H
H= 2160/216
H= 10 m
So the height of the Tank 3= 10 m
To keep the fish healthy, there should be the correct ratio of water to fish in the tank. One recommended ratio is 9 L of water for every 2 fish. Find the volume of Tank 4. Then use the equivalencies 1 cm3 = 1 mL and 1,000 mL = 1 L to find how many fish can be safely kept in Tank 4.
Volume of Tank 4 = LWH
= 72×55×40
= 1,58,400 cm3
As 1 cm3 = 1 mL and 1,000 mL = 1 L
1,58,400 cm3 = 1,58,400 mL and 1,58,400 mL = 158.4 L
So tank can keep safely (158.4÷ 9)×2
= (17.6)× 2 = 35.2
= 35 Fishes
Use Reasoning Give another set of dimensions for a tank that would have the same volume as Tank 2. Explain how you found your answer.
Answer: Another set of dimensions for a tank that would have the same volume as Tank 2 is 8m by 8m by 6m.
So when we multiply the product will be 384
_______ \(\frac{□}{□}\) m3
Answer: 150 5/16 m3
Explanation: Volume= Length×width×height
= 5× 13/4 × 37/4
= 2405/16
= 150 5/16 m3
Answer: 27 1/2 in.3
= 5 1/2 × 2 1/2 × 2
= 11/2 × 5/2 × 2
= 27 1/2 in.3
_______ \(\frac{□}{□}\) mm3
Answer: 91 1/8 mm3
= 4 1/2 × 4 1/2 × 4 1/2
= 91 1/8 mm3
Answer: 112 1/2 ft3
= 112 1/2 ft3
Answer: 36 m3
The area of shaded face is Length × width= 8 m2
Volume of the prism= Length×width×height
= 8 × 4 1/2
= 8 × 9/2
Explanation: Volume of the prism= Length×width×height
= 2 1/4 × 6 × 2 1/4
= 9/4 × 6 × 9/4
A cereal box is a rectangular prism that is 8 inches long and 2 \(\frac{1}{2}\) inches wide. The volume of the box is 200 in.3. What is the height of the box?
_______ in.
Answer: H= 10 in
Explanation: As volume = 200 in.3. So
V= LWH
200= 8 × 2 1/2 × H
200= 8 × 5/2 × H
200= 20 × H
H= 10 in
A stack of paper is 8 \(\frac{1}{2}\) in. long by 11 in. wide by 4 in. high. What is the volume of the stack of paper?
Explanation: The volume of the stack of paper= LWH
= 8 1/2 × 11 × 4
= 17/2 × 11 × 4
Explain how you can find the side length of a rectangular prism if you are given the volume and the two other measurements. Does this process change if one of the measurements includes a fraction?
Answer: We can find the side length of a rectangular prism if you are given the volume and the two other measurements by dividing the value of the volume by the product of the values of width and height of the prism. And the process doesn't change if one of the measurements include a fraction.
A kitchen sink is a rectangular prism with a length of 19 \(\frac{7}{8}\) inches, a width of 14 \(\frac{3}{4}\) inches, and height of 10 inches. Estimate the volume of the sink.
Explanation: Length = 19 7/8 as the number was close to 20 and width 14 3/4 which is close to 15 and height is 10
So Volume= LBH
= 20 × 15 × 10
A storage container is a rectangular prism that is 65 centimeters long and 40 centimeters wide. The volume of the container is 62,400 cubic centimeters. What is the height of the container?
Answer: H= 24 cm
Explanation: Volume of container= LBH
Volume= 62,400 cubic centimeters
62,400 = 65× 40 × H
62,400 = 2600 × H
H= 62,400/ 2600
H= 24 cm
Carrie started at the southeast corner of Franklin Park, walked north 240 yards, turned and walked west 80 yards, and then turned and walked diagonally back to where she started. What is the area of the triangle enclosed by the path she walked?
Answer: 9,600 yd2
Area of triangle= 1/2 bh
= 1/2 × 240 × 80
= 240 × 40
= 9,600 yd2
The dimensions of a rectangular garage are 100 times the dimensions of a floor plan of the garage. The area of the floor plan is 8 square inches. What is the area of the garage?
Answer: 80,000 in2
Explanation: As 1 in2= 10,000 in2, so area of the floor plan 8 in
= 8×10000
= 80,000 in2
Shiloh wants to create a paper-mâché box shaped like a rectangular prism. If the box will be 4 inches by 5 inches by 8 inches, how much paper does she need to cover the box?
Explanation: Area of the rectangular prism= 2(wl+hl+hw)
= 2(4×5 + 5×8 + 8×4)
A box is filled with 220 cubes with a side length of \(\frac{1}{2}\) unit. What is the volume of the box in cubic units?
Answer: 27.5 cubic units.
Explanation: The volume of a cube side is (1/2)3 = 1/8
So 220 cubes= 220× 1/8
= 27.5 cubic units.
An aquarium tank in the shape of a rectangular prism is 60 cm long, 30 cm wide, and 24 cm high. The top of the tank is open, and the glass used to make the tank is 1 cm thick. How much water can the tank hold?
Answer: So tank can hold 37,352 cm3
Explanation: As Volume= LBH
Let's find the inner dimensions of the tank, so 60-2 × 30-2 × 24-1
= 37,352 cm3
What if, to provide greater strength, the glass bottom were increased to a thickness of 4 cm? How much less water would the tank hold?
Answer: 4,872 cm3
Explanation: As the glass bottom was increased to a thickness of 4 cm, 60-2 × 30-2 × 24-4
So the tank can hold 37,352- 32,480= 4,872 cm3
An aquarium tank in the shape of a rectangular prism is 40 cm long, 26 cm wide, and 24 cm high. If the top of the tank is open, how much tinting is needed to cover the glass on the tank? Identify the measure you used to solve the problem.
Answer: 4,208 cm3 tinting needed to cover the glass on the tank.
The lateral area of the two faces is 26×24= 624 cm2
The lateral area of the other two faces is 40×24= 960 cm2
And the area of the top and bottom is 40×26= 1040 cm2
So the surface area of the tank without the top is 2×624 + 2×960 + 1040
= 1,248+1,920+1,040
= 4,208 cm3
The Louvre Museum in Paris, France, has a square pyramid made of glass in its central courtyard. The four triangular faces of the pyramid have bases of 35 meters and heights of 27.8 meters. What is the area of glass used for the four triangular faces of the pyramid?
Explanation: The area of one face is 1/2 × 35 × 27.8= 486.5 m2
And the area of glass used for the four triangular faces of the pyramid is 4×486.5= 1946 m2
A rectangular prism-shaped block of wood measures 3 m by 1 \(\frac{1}{2}\) m by 1 \(\frac{1}{2}\) m. How much of the block must a carpenter carve away to obtain a prism that measures 2 m by \(\frac{1}{2}\) m by \(\frac{1}{2}\) m?
Answer: 6 1/4 m3
Explanation: The volume of the original block= LWH
= 3 × 1 1/2 × 1 1/2
= 6 3/4 m2
And volume of carpenter carve is 2× 1/2 × 1/2
= 1/2 m2
So, the carpenter must carve 27/4 – 1/2
The carpenter (Problem 5) varnished the outside of the smaller piece of wood, all except for the bottom, which measures \(\frac{1}{2}\) m by \(\frac{1}{2}\) m. Varnish costs $2.00 per square meter. What was the cost of varnishing the wood?
$ _______
Answer: $8.50
Explanation: The area of two lateral faces are 2×1/2= 1 m2
The area of the other two lateral faces are 2×1/2= 1 m2
The area of the top and bottom is 1/2×1/2= 1/4 m2
And the surface area is 2×1 + 2×1 + 1/4
= 2+2+1/4
= 4.25 m2
And the cost of vanishing the wood is $2.00× 4.25= $8.50
A wax candle is in the shape of a cube with a side length of 2 \(\frac{1}{2}\) in. What volume of wax is needed to make the candle?
Explanation: The Volume of wax is needed to make the candle is= LWH
Describe A rectangular prism-shaped box measures 6 cm by 5 cm by 4 cm. A cube-shaped box has a side length of 2 cm. How many of the cube-shaped boxes will fit into the rectangular prismshaped box? Describe how you found your answer.
Answer: 12 cube-shaped boxes
Explanation: As 6 small boxes can fit on the base i.e 6 cm by 5 cm, as height is 4cm there can be a second layer of 6 small boxes. So, there will be a total of 12 cube-shaped boxes and will fit into a rectangular prism-shaped box
Justin is covering the outside of an open shoe box with colorful paper for a class project. The shoe box is 30 cm long, 20 cm wide, and 13 cm high. How many square centimeters of paper are needed to cover the outside of the open shoe box? Explain your strategy
The area of the two lateral faces of the shoebox is 20×13= 260 cm2
The area of another two lateral faces of the shoebox is 30×13= 390 cm2
The area of the top and bottom is 30×20= 600 cm2
So, the surface area of the shoebox without the top is 2×260 + 2× 390 + 600
Read each problem and solve.
The outside of an aquarium tank is 50 cm long, 50 cm wide, and 30 cm high. It is open at the top. The glass used to make the tank is 1 cm thick. How much water can the tank hold?
Answer: So water tank can hold 66,816 cm3
Explanation: The volume of inner dimensions of the aquarium is 50-2 × 50-2 × 30-1
So water tank can hold 66,816 cm3
Arnie keeps his pet snake in an open-topped glass cage. The outside of the cage is 73 cm long, 60 cm wide, and 38 cm high. The glass used to make the cage is 0.5 cm thick. What is the inside volume of the cage?
Answer: The volume of the cage is 1,59,300 cm3
Explanation: The volume of inner dimensions is 73-1 × 60-1 × 38-0.5
= 72×59×37.5
So, the volume of the cage is 1,59,300 cm3
A display number cube measures 20 in. on a side. The sides are numbered 1–6. The odd-numbered sides are covered in blue fabric and the even-numbered sides are covered in red fabric. How much red fabric was used?
Answer: 1200 in.2
Explanation: The area of each side of a cube is 20×20= 400 in.2, as there are 3 even-numbered sides on the cube. So there will be
3×400= 1200 in.2
The caps on the tops of staircase posts are shaped like square pyramids. The side length of the base of each cap is 4 inches. The height of the face of each cap is 5 inches. What is the surface area of the caps for two posts?
Explanation: The area of the base is 4×4= 16 in.2
The area of one face is 1/2×5×4= 10 in.2
The surface area of one cap is 16+4×10
And the surface area of the caps for two posts is 2×56= 112 in.2
A water irrigation tank is shaped like a cube and has a side length of 2 \(\frac{1}{2}\) feet. How many cubic feet of water are needed to completely fill the tank?
Explanation: Volume= LWH
Write and solve a problem for which you use part of the formula for the surface area of a triangular prism.
Answer: In a triangular prism, the triangular end has a base of 5cm and the height is 8 cm. The length of each side is 4 cm and the height of the prism is 10 cm. What is the lateral area of this triangular prism?
Explanation: The area of two triangular faces is 1/2 × 5 × 8
The area of two rectangular faces is 4×10= 40 cm2
The lateral area is 2×20+2×40
Maria wants to know how much wax she will need to fill a candle mold shaped like a rectangular prism. What measure should she find?
Answer: Maria needs to find the volume of the mold.
The outside of a closed glass display case measures 22 inches by 15 inches by \(\frac{1}{2}\) inches. The glass is 12 inch thick. How much air is contained in the case?
Explanation: The inner dimensions are 22-1× 15-1 × 12- 1/2
= 21 ×14×23/2
= 3381 in.3
A trapezoid with bases that measure 5 centimeters and 7 centimeters has a height of 4.5 centimeters. What is the area of the trapezoid?
Answer: 27 cm2
Explanation: Area of trapezoid= 1/2 ×(7+5)×4.5
Sierra has plotted two vertices of a rectangle at (3, 2) and (8, 2). What is the length of the side of the rectangle?
_______ units
Answer: 5 units.
Explanation: The length of the side of the rectangle is 8-3= 5 units.
Answer: 104 m2
Explanation: The area of the base 4×4= 16
The area of the one face is 1/2 × 4 × 11
A shipping company has a rule that all packages must be rectangular prisms with a volume of no more than 9 cubic feet. What is the maximum measure for the height of a box that has a width of 1.5 feet and a length of 3 feet?
_______ feet
Answer: 2 feet.
Explanation: As given volume = 9 cubic feet
So 1.5×3×H < 9
4.5×H < 9
H< 9/4.5
and H<2
So maximum measure for the height of the box is 2 feet.
Elaine makes a rectangular pyramid from paper.
The base is a _____. The lateral faces are _____.
The base is a ___________ .
The lateral faces are ___________ .
The base is a rectangle.
The lateral faces are triangles.
Darrell paints all sides except the bottom of the box shown below.
Select the expressions that show how to find the surface area that Darrell painted. Mark all that apply.
a. 240 + 240 + 180 + 180 + 300 + 300
b. 2(20 × 12) + 2(15 × 12) + (20 × 15)
c. (20 × 12) + (20 × 12) + (15 × 12) + (15 × 12) + (20 × 15)
d. 20 × 15 × 12
Answer: b,c
Explanation: The expressions that show how to find the surface area is 2(20 × 12) + 2(15 × 12) + (20 × 15), (20 × 12) + (20 × 12) + (15 × 12) + (15 × 12) + (20 × 15)
A prism is filled with 44 cubes with \(\frac{1}{2}\)-unit side lengths. What is the volume of the prism in cubic units?
_______ \(\frac{□}{□}\) cubic unit
As there are 44 cubes so 44×0.125=5.5 cubic units.
A triangular pyramid has a base with an area of 11.3 square meters, and lateral faces with bases of 5.1 meters and heights of 9 meters. Write an expression that can be used to find the surface area of the triangular pyramid.
Answer: 11.3+ 3 × 1/2+ 5.1×9
Explanation: The expression that can be used to find the surface area of the triangular pyramid is 11.3+ 3 × 1/2+ 5.1×9
Jeremy makes a paperweight for his mother in the shape of a square pyramid. The base of the pyramid has a side length of 4 centimeters, and the lateral faces have heights of 5 centimeters. After he finishes, he realizes that the paperweight is too small and decides to make another one. To make the second pyramid, he doubles the length of the base in the first pyramid.
For numbers 5a–5c, choose Yes or No to indicate whether the statement is correct.
5a. The surface area of the second pyramid is 144 cm2.
5b. The surface area doubled from the first pyramid to the second pyramid.
5c. The lateral area doubled from the first pyramid to the second pyramid.
5a. ___________
5b. ___________
5c. ___________
5a. True.
5b. False
5c. True.
The area of the base is 4×4= 16 cm2.
The surface area of the First pyramid is 16+ 4×10
The surface area od the second pyramid is 64+ 4×20
Identify the figure shown and find its surface area. Explain how you found your answer.
The area of the base is 9×9= 81 in2
The area of one face is 1//2 × 16× 9
The surface area of a square pyramid is 81+ 4× 72
Dominique has a box of sewing buttons that is in the shape of a rectangular prism.
The volume of the box is 2 \(\frac{1}{2}\) in. × 3 \(\frac{1}{2}\) in. × _____ = _____.
Answer: 17.5 in3
Explanation: The volume of the box is 2 1/2 × 3 1/2 × 2
= 5/2 × 7
= 17.5 in3
Emily has a decorative box that is shaped like a cube with a height of 5 inches. What is the surface area of the box?
Explanation: Surface area of the box is 6 a2
So 6 × 52
= 6×5×52
Albert recently purchased a fish tank for his home. Match each question with the geometric measure that would be most appropriate for each scenario.
Select the expressions that show the volume of the rectangular prism. Mark all that apply.
a. 2(2 units × 2 \(\frac{1}{2 }\) units) + 2(2 units × \(\frac{1}{2}\) unit) + 2(\(\frac{1}{2}\) unit × 2 \(\frac{1}{2}\) units)
b. 2(2 units × \(\frac{1}{2}\) unit) + 4(2 units × 2 \(\frac{1}{2}\) units)
c. 2 units × \(\frac{1}{2}\) unit × 2 \(\frac{1}{2}\) units
d. 2.5 cubic units
Answer: c, d
Explanation: 2 units ×1/2 unit × 2 1/2 units and 2.5 cubic units
For numbers 11a–11d, select True or False for the statement.
11a. The area of face A is 8 square units.
11b. The area of face B is 10 square units.
11c. The area of face C is 8 square units.
11d. The surface area of the prism is 56 square units.
11a. ___________
11b. ___________
11c. ___________
11d. ___________
11a. True.
11b. True.
11c. False.
11d. False.
The area of the face A is 4×2= 8 square units
The area of the face B is 5×2= 10 square units
The area of the face C is 5×4= 20 square units
So the surface area is 2×8+2×10+2×20
Stella received a package in the shape of a rectangular prism. The box has a length of 2 \(\frac{1}{2}\) feet, a width of 1 \(\frac{1}{2}\) feet, and a height of 4 feet.
Stella wants to cover the box with wrapping paper. How much paper will she need? Explain how you found your answer
Answer: 39.5 ft2
The area of two lateral faces is 4 × 2 1/2
The area of another two lateral faces is 4 × 1 1/2
The area of the top and bottom is 2 1/2 × 1 1/2
= 3 3/4 ft2
So Stella need 2×10+ 2×6 + 2 × 15/4
= 20+ 12+15/2
= 20+12+7.5
= 39.5 ft2
Can the box hold 16 cubic feet of packing peanuts? Explain how you know
Answer: The box cannot hold 16 cubic feet of the packing peanuts
Explanation: Volume = LWH
= 2 1/2 ×1 1/2 × 4
= 5/2 × 3/2 ×4
So the box cannot hold 16 cubic feet of the packing peanuts.
A box measures 6 units by \(\frac{1}{2}\) unit by 2 \(\frac{1}{2}\) units.
For numbers 13a–13b, select True or False for the statement.
13a. The greatest number of cubes with a side length of \(\frac{1}{2}\) unit that can be packed inside the box is 60.
13b. The volume of the box is 7 \(\frac{1}{2}\) cubic units.
13a. True
Length is 12 × 1/2= 6 units
Width is 1× 1/2= 1/2 units
Height is 5× 1/2= 5/2 units
So, the greatest number of cubes with a side length of 1/2 unit that can be packed inside the box is 12×1×5= 60
As there are 60 cubes so 60×0.125= 7.5cubic units.
Bella says the lateral area of the square pyramid is 1,224 in.2. Do you agree or disagree with Bella? Use numbers and words to support your answer. If you disagree with Bella, find the correct answer.
Area= 4× 1/2 bh
= 4× 1/2 × 18 × 25
= 2× 18 × 25
So lateral area is 900 in2, so I disagree
Lourdes is decorating a toy box for her sister. She will use self-adhesive paper to cover all of the exterior sides except for the bottom of the box. The toy box is 4 feet long, 3 feet wide, and 2 feet high. How many square feet of adhesive paper will Lourdes use to cover the box?
The area of two lateral faces is 4×2= 8 ft2
The area of another two lateral faces is 3×2= 6 ft2
The area of the top and bottom is 4×3= 12 ft2
So Lourdes uses to cover the box is 2×8 + 2×6 + 12
Gary wants to build a shed shaped like a rectangular prism in his backyard. He goes to the store and looks at several different options. The table shows the dimensions and volumes of four different sheds. Use the formula V = l × w × h to complete the table.
Length of shed 1= 12 ft
Width of shed 2= 12 ft
Height of shed 3= 6 ft
Volume of shed 4= 1200 ft3
Volume of shed1= 960 ft
So 960= L×10×8
960= 80×L
L= 960/80
L= 12 ft
Volume of shed2= 2160 ft
So 2160= 18×W×10
960= 180×W
W= 2160/180
W= 12 ft
So 288= 12×4×H
288= 48×H
H= 288/48
W= 6 ft
Volume of shed2= 10×12×10
So V= 10×12×10
V= 1200 ft3
Tina cut open a cube-shaped microwave box to see the net. How many square faces does this box have?
_______ square faces
Answer: The box has 6 square faces.
Charles is painting a treasure box in the shape of a rectangular prism.
Which nets can be used to represent Charles' treasure box? Mark all that apply.
Answer: a and b can be used to represent Charle's treasure box.
Julianna is lining the inside of a basket with fabric. The basket is in the shape of a rectangular prism that is 29 cm long, 19 cm wide, and 10 cm high. How much fabric is needed to line the inside of the basket if the basket does not have a top? Explain your strategy.
Explanation: The surface area= 2(WL+HL+HW)
The surface area of the entire basket= 2(19×29)+2(10×29)+2(10×19)
= 2(551)+2(290)+2(190)
= 1102+580+380
The surface area of the top is 29×19= 551
So Julianna needs 2062-551= 1511 cm2


text:
Companies' Anti-Slavery Performance Improves, iPoint-funded Study Reveals
American Eagle Outfitters, HP, Intel, and Burberry top list of 1,909 evaluated brands
Submitted by: iPoint-systems gmbh
Categories: Human Rights, Research, Reports & Publications
Posted: Mar 07, 2017 – 10:00 AM EST
CA-TISCA Report 2016 - Front Page
REUTLINGEN, GERMANY, Mar. 07 /CSRwire/ - Social and environmental compliance, sustainability, and digital circular economy expert iPoint is excited to announce the release of a new comprehensive benchmarking report which evaluates brands on their anti-slavery compliance with the California Transparency in Supply Chains Act of 2010 (CA-TISCA). Funded by iPoint and prepared by Development International (DI), a not-for-profit organization specialized in evaluations, the report rates the legal compliance, affirmative practice, and transparency of 1,909 companies' anti-human trafficking and slavery-related disclosure statements of 2016.
Improvements on All Fronts
The study indicates that the companies in focus have improved on all fronts as compared to reporting year 2015. "More companies have a statement, more are compliant, and more pro-active initiative is being taken by these businesses in their efforts to responsibly produce and source goods which they sell in California," Dr. Chris Bayer, DI's Principal Investigator and co-author of the study, states.
CA-TISCA requires retailers and manufacturers doing business in the state of California with annual worldwide gross receipts exceeding $100 million to publicly disclose the measures they have taken to eradicate modern-day slavery and human trafficking in their supply chains. The companies subject to the Californian law include U.S. as well as foreign companies with a combined global revenue of $48.4 trillion in 2016.
For 2016, the study measured a noticeable improvement in companies' anti-slavery compliance and actions as compared to the previous year. For example, in 2015, only 41% percent of the 1,504 evaluated companies had a corporate disclosure score on or above the 70% mark. In 2016, 52% of the 1,909 evaluated companies had a disclosure score above 70%. According to Bayer, "This increase not only indicates that legal compliance with this particular anti-slavery disclosure law is gradually improving, it also underlines that the issue of modern day slavery is receiving increased visibility around the globe."
2016 Top Scorers
Among the 20 companies which received a combined compliance, affirmative, and transparency score of 86% and above are American Eagle Outfitters (95%), HP (93%), Intel (92%), Burberry (90%), Brooks Sports (90%), Patagonia (89%), GAP (88%), Papyrus (88%), Bath & Body Works (87%), Vans (87%), and Apple (86%). One top 20 company in particular stands out as to the significant progress it has made since 2015: NXP Semiconductors N.V. (87%) has shown a 71% improvement in the compliance area, and an 80% improvement concerning its affirmative practice. In November 2016, the Dutch global semiconductor manufacturer was announced as one of the winners of Thomson Reuters Foundation's high-profile Stop Slavery Award, which recognizes businesses that have excelled in efforts to eradicate forced labor from their supply chains.
Evolving Transnational and Cross-Sector Efforts
"There are definitely flagship brands and industries leading the way in the anti-slavery area, and recent as well as upcoming laws in France, Australia, and other countries indicate the encouraging shift in the number of countries that are engaging on the issue", iPoint-CEO Joerg Walden emphasizes. "However, in order to effectively tackle and eradicate human trafficking and modern-day slavery around the globe, joint efforts, learning from peers, supply-chain wide collaboration and cross-sector solutions such as the electronic Labor Rights Template (eLRT) are key."
"The catch 22 is that brands can lead, but cannot complete the task in isolation," Julia Ormond highlights in the report's foreword. "Conversely, self-acknowledgement of slavery risk in supply chains would beget supply chain mapping, sector and cross-sector partnerships; to enable new solutions and anti-slavery measures to evolve and prove their value." Ormond is founder and president of the Alliance to stop Slavery and End Trafficking (ASSET), which was instrumental in passing the California Transparency in Supply Chains Act and the UK Modern Slavery Act (2015).
The full report, entitled "Corporate Compliance with the California Transparency in Supply Chains Act: Anti-Slavery Performance in 2016", can be downloaded from the iPoint website at http://www.ipoint-systems.com/ca-tisca-2016/
Evaluated companies can also request their individual scorecards with a breakdown of their disclosure compliance, affirmative practice, and transparency score, from this website.
Katie Boehme Head of Corporate Communications
Phone: 004971211448960
iPoint-systems gmbh
iPoint is a leading provider of software and consulting for environmental and social product compliance, and sustainability. Tens of thousands of companies around the globe rely on iPoint for managing, tracking, analyzing, and reporting data across the whole value creation network. iPoint's softw...
New Anti-Slavery Reporting and Risk Management Tool Launched
iPoint Recognized as Top Compliance Solution Provider 2019
CSR Reporting Under EU Law Is Highest for Gender and Lowest for Human Rights Matters, Study Reveals
Free Webinar: The 2016 Anti-Slavery Compliance Benchmarking Study – Trends and Good Practices

redpajama_set_name: RedPajamaCommonCrawl


If you are a goalkeeper (or a parent of a goalkeeper) and you are looking for a VIP Experience to help you achieve your goalkeeping dreams, this is the opportunity you have been waiting for.
GOALKEEPER NUMBERS: So this is truly a VIP GK Experience and J4K can assess you, develop you and look to potentially showcase you to our vast amount of national and or international contacts, numbers are STRICTLY LIMITED to a minimum of 3 keepers to a maximum of just 6.
TRAINING: You will be put through your paces to see just what it is like to train at the top level, just like a professional goalkeeper. This will also help you if you are looking to gain a college scholarship, because if you understand the tempo needed to train like a professional goalkeeper, you will be ahead of 99% of your college goalkeeper competition.
DEVELOPMENT: As well as putting you through your paces, we will guarantee by the time you have finished your VIP experience, you will leave a better goalkeeper.
MENTAL STRENGTH: J4k has helped thousands of keepers achieve their dreams, and without doubt a solid mind set beats ability hands down. It is all well and good developing to be a better goalkeeper, but can you perform when you are under pressure? This is sadly where 99% of keepers fail. They have the ability, but when the pressure is on, they just have not got the mental toughness to perform under pressure.
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Obviously, there will always be goalkeeper coaches who have not had the personal experiences themselves playing under pressure, but still have exceptional talent to help their goalkeeper students succeed, but this will be in the minority.
RAY NEWLAND: is the founder of Just4keepers and who has helped thousands of goalkeepers over the years achieve their dreams, whether getting to professional soccer clubs or gaining a college scholarship.
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He has coached and played at the highest level, playing professionally in goal for over a decade for premiership clubs like Everton FC, and also coaching at International level.
PAUL CRICHTON: is an English former professional footballer and is now a highly experienced and sought after goalkeeper coach.
Aa a player he was a goalkeeper from 1986 to 2011. During his playing career Crichton notably had lengthy spells with Grimsby Town, Doncaster Rovers, West Bromwich Albion and Burnley having also played as a professional for Nottingham Forest, Notts County, Darlington, Peterborough United, Swindon Town, Rotherham United, Aston Villa and Norwich City. He then moved into the Non-League game where he turned out for York City, Gainsborough Trinity, Stafford Rangers, Leigh RMI and Accrington Stanley.
Although never officially announcing his retirement, Crichton moved into coaching in 2005 and has since been the goalkeeping coach of Gillingham, Cambridge United, King's Lynn, Brighton & Hove Albion and Sheffield United as well as been registered as a player with each club.
IT IS IMPORTANT TO NOTE BOTH GOALKEEPER COACHES NOW CALL USA HOME AND OUR COMMITTED TO HELPING US GOALKEEPERS, GK COACHES AND SOCCER CLUBS.
As the J4K VIP Experience runs year-round at our national goalkeeper center here in Florida, when you book on, we will give you a list of dates that are available. You simply pick the one best for you. In the event you cannot make any of the available dates, J4K will immediately refund your booking payment.
Also, when you book on, whether you attend or not, as a thank you for trusting J4K, we will give you access to a website where you will get 50% off all your goalkeeper gloves FOR LIFE!!!. So worth booking on just for this.
VERY IMPORTANT: even though training is in a very fun and friendly atmosphere, please remember the J4K VIP training is intense and most keepers would not have experienced this intensity, so only book on if you are prepared to come and put a 1000% effort into your training.
We look forward to helping you achieve your dreams!
Price is $499 for the full weeks training 8am til 4pm, off and on the field, plus classroom education and our money back guarantee you will not have experienced this type of "on and off' the field goalkeeper training AND development!!!.
Another bonus, is most of the training gets filmed, so by the time you have finished with you VIP experience, you will have your own promotional video. Some organisations charge as much $2000 for what you will get as part of this VIP experience.
Please Note: Our accommodation is currently under construction, so we will recommend local hotels once booked.


text:
Authorities keep distance, yet work with armed border group
Published Thu Apr 25 2019 01:54:07 GMT+0000 (UTC)
by By CEDAR ATTANASIO and ELLIOT SPAGAT
SUNLAND PARK, New Mexico (AP) — Authorities on the U.S.-Mexico border have distanced themselves from an armed civilian group that detains asylum-seeking families, but the United Constitutional Patriots have never been shy about saying they work with Border Patrol agents.
After its activities drew widespread criticism, the group was thrown out of its camp this week for trespassing in Sunland Park, New Mexico, a suburb of El Paso, Texas. Frequent social media posts show masked men in combat fatigues chasing migrants and ordering them to stay put until border agents arrive. Videos capture agents taking migrants into custody.
Jim Benvie, a spokesman for the group, said in a March 7 video on Facebook titled "Hunting illegals/us Mexico border" that he agreed to join the effort because he was "looking for action and video." He encouraged anyone who "wants to do the militia thing" to come to Sunland Park — with a gun, if available.
"Everything is registered, so you work in hand with the Border Patrol," he said.
Armed civilian groups have been an intermittent presence on the border for years, portraying themselves as auxiliaries to the Border Patrol and operating in areas where agents are not stationed. As the videos show, U.S. authorities keep them at arm's length while also responding to reports of people entering the country illegally.
Customs and Border Protection, which includes the Border Patrol, said Friday on Twitter that it "does not endorse or condone private groups or organizations that take enforcement matters into their own hands."
"Interference by civilians in law enforcement matters could have public safety and legal consequences for all parties involved," the agency said.
The Sunland Park police chief said he had told the small group they could stay as long as they did not try to arrest anyone or hold anybody at gunpoint.
Three Democratic members of Congress, including Veronica Escobar of El Paso, wrote FBI Director Christopher Wray asking for an investigation into the presence of armed civilians and any assistance from U.S. authorities.
"The right to stop and detain should be reserved to law enforcement," they wrote.
Border Patrol spokesman Carlos Antunez said Wednesday that agents will investigate such groups only if a migrant complains, which has not happened with the United Constitutional Patriots.
If the group is detaining migrants, "that's all they're doing," Antunez said. "At that point, we take charge ... We end up arresting the people that entered illegally, and then we take it from there."
The group's leader, Larry Hopkins, was arrested last weekend on federal weapons charges. Hopkins, 69, was transferred Tuesday out of a New Mexico jail after suffering unspecified non-life threatening injuries, the Dona Ana County Sheriff's Office said.
Benvie narrated a March 13 video under the words "Caught another group of well-dressed illegals." He said the Border Patrol will arrive "in a minute" and then showed an agent taking a small group into custody. Three days later, he posted another video under the heading "Detained a man with a baby!" As an agent arrived, Benvie said, "The border is overrun. We're being invaded."
In another video, he said: "It's a war zone, guys. This is like the Wild West, but we caught these guys right away."
A video that drew strong criticism included a man who could be heard reporting on a group of at least 200 migrants. Benvie alerted viewers when the Border Patrol arrived.
The group was thrown out of its camp Tuesday after Union Pacific Railroad posted no-trespassing signs nearby.
"Base camp is relocating, new videos coming soon!" Benvie wrote the next day.
Two El Paso men who were fishing on the Rio Grande in Sunland Park were skeptical of the group.
"We all look Mexican. How are they going to know the difference?" asked Angel Martinez, a 34-year-old factory worker. "That's what Border Patrol is for."
His friend and fellow fisherman Henry Aguilar, a delivery driver, once worked at an immigration detention center where he came into contact with hardened Central American gang members from MS-13, who he's glad were deported. But the families being detained by the militia "are not even threats," he said.
In the past, vigilante patrols interrupted his fishing farther downstream, near where the United Constitutional Patriots plan to relocate. He believes a member of the group approached him last summer.
"He told us we couldn't fish there. I told him to identify himself, and he refused to do so," Aguilar recalled. "He had camo gear on, and he had a hat, and he was covered from the nose down."
Spagat reported from San Diego.
Sunland Park Police Chief Javier Guerra speaks from his headquarters in Sunland Park, N.M., Tuesday, April 23, 2019. Guerra's department assisted with the eviction of a militia group that was patrolling the border, detaining immigrants, and posting videos of their actions on Facebook. The groups was made to leave after the police received a complaint that they were on private property. (AP Photo/Cedar Attanasio)
This April 20, 2019 booking photo from the Dona Ana County Sheriff's Office shows Larry Hopkins. Authorities say that Hopkins, 69, the leader of a group that has detained asylum-speaking migrants along the U.S.-Mexico border, was injured while he was jailed in Las Cruces, N.M., after being arrested on federal weapons charges. The Dona Ana County Sheriff's Office said Wednesday, April 24, 2019 in a statement that Hopkins was transferred Tuesday out of the county jail after suffering non-life threatening injuries Monday night. (Dona Ana County Sheriff's Office via AP)
Members of the United Constitutional Patriots plan their next move after being evicted from Union Pacific land where they were camped for months watching for asylum seekers crossing the border Tuesday, April 23, 2019, in Anapra, N.M. (Mark Lambie/The El Paso Times via AP)
"Viper," a member of the United Constitutional Patriots stands dejected after Union Pacific Police evicted the group from their camp in Anapra, N.M., Tuesday, April, 23, 2019. The group was camping on Union Pacific land. (Mark Lambie/The El Paso Times via AP)
An trailer used by members of the United Constitutional Patriots sits a quarter mile from a barrier that marks the U.S.-Mexico border Tuesday, April 23, 2019, in Sunland Park, N.M., hours before its occupants were evicted by police. Members of the United Constitutional Patriots gained national attention after filming themselves detaining immigrants who cross the border to the east where the wall ends. (AP Photo/Cedar Attanasio)
"Viper," a member of the United Constitutional Patriots stands dejected after Union Pacific Police evicted the group from their camp in Anapra, N.M., Tuesday, April, 23, 2019. The group was camping on Union Pacific land. Group spokesman Jim Benvie said in a social media post that the group will relocate and that operations will continue. (Mark Lambie/The El Paso Times via AP)
Boundary Monument 1, a historic U.S.-Mexico border marker, seen from Sunland Park, N.M., Wednesday, April 24, 2019. This unfenced area of the border west of the Rio Grande was shown in videos shot by the United Constitutional Patriots, a citizen immigration patrol that says it cooperates with the U.S. Border Patrol. (AP Photo/Cedar Attanasio)
An self-styled Patriot stands a quarter mile from a barrier that marks the U.S.-Mexico border Tuesday, April 23, 2019, in Sunland Park, N.M., hours before being removed from his group's campsite by police. Members of the United Constitutional Patriots gained national attention after filming themselves detaining immigrants who cross the border to the east where the wall ends. (AP Photo/Cedar Attanasio)
A Union Pacific Police unit sits guard as members of the United Constitutional Patriots group vacates their camp near the border in Anapra, N.M., Tuesday, April, 23, 2019. Sunland Park police and security officers with the railroad company told members of the United Constitutional Patriots on Tuesday they needed to move their trailers and equipment. (Mark Lambie/The El Paso Times via AP)


text:
schools in gurgaon
Schools in Gurgaon - Lancers International School is one of the best schools in Gurgaon which offers IB schools in Gurgaon.Lancers International School is a co-educational international boarding school for students from ages 16 months to 18 years. Lancers International School is one of the leading IB Schools in Gurgaon. Lancers is a Boarding/ Day Boarding School in Gurgaon. We offer the IB Programme and the IGCSE Programme. Being one of the top boarding schools in Gurgaon, we offer PYP in Primary School, MYP in Middle School, and DP in Senior School. Our Primary School is also one of the most prestigious Daycare Schools in Gurgaon. Schools in Gurgaon offer a different kind of environment and curriculum. We strongly suggest parents to visit schools of their choice to see what best fits their needs. We are the only school in Gurgaon with its student body representing 45 nationalities, making it one of the most diverse, International Schools in the city.
Personalised education,
because we all learn differently
Lancers Global
Working with LIS
Health Advisory
Welcome To Boarding
Home Admission
PYP E-Learning
Baby Centre
PYP Exhibition
External Assessments
IB MYP
IB MYP Curriculum
IB MYP E-Assessment
IB MYP Recognition
Community & Personal Projects
Cambridge International Certificate in Education (ICE)
IBDP Curriculum
Individual Mentoring Program
CAS Program
Extended Essay Timeline
Little ABLE
At Lancers International School, we lay a strong emphasis on academics and extra-curricular activities, within a culture of numerous possibilities. Here, students express their opinions freely and are offered a supportive environment, which allows them to grow into mature and sensitive adults.
Lancers International School welcomes applications from bright, diverse students throughout the calendar year. Our admissions representatives can help you decide the best time to apply. We build an applicant pool with a purpose to include a good flow of opportunities for a wide range of applicants. We make time to work with every inquiry and applicant to guide them with when admission might be possible.
We understand that choosing the right school for your child can be a daunting task. This is especially true if you're moving across the city or across the world, and want to give your child a school with a diverse environment and a holistic way of teaching. That's one of the main reasons why we encourage both parents and children to visit our school prior to taking admission, meet with the faculty and understand the true spirit of Lancers before joining the school.
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Under the computer networks option students must satisfy the MS, Electrical Engineering requirements with the exception that only 15 units of EE are required.
With the exception of EE 503 , the fundamental courses may also be satisfied by having passed EE placement exams.
If a fourth required course is taken it can be counted toward elective credit.
Any other course must be approved by a faculty adviser.


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text:
Career and Life Design
Empowering careers, learning and performance
Career and Life Coaching
High-Performing Teams
Birkman Solutions
Jungian Sandplay
Bringing Kindness to Work!
careernlifedesign January 28, 2020	 June 9, 2020
Home Kindness Bringing Kindness to Work!
"What is your job?" This question can change your life!
careernlifedesign Kindness January 28, 2020	 June 9, 2020
According to Dr Kelli Harding, Physician and Author of The Rabbit Effect: Live Longer, Happier, and Healthier with the Groundbreaking Science of Kindness, a major determinant of our health is our social relationships and our connection to our community. She refers to this as a hidden factor of health.
Working in emergency room in New York, Dr Harding observed that some patients who were seriously ill were doing much better and thriving in many respects compared with some patients who had treatable conditions. She found that our day-to-day connections with people in our lives made a big difference to our health and that loneliness can affect our health adversely.
The book title "The Rabbit Effect" takes its name from a 1978 study on rabbit heart health. The study found that a group of rabbits was in much better health than others because they were petted and talked to and treated with love and kindness by the researcher. Dr Harding's research found that kindness can have a healing effect and an effect on wellbeing.
Everyone can make a difference when they reach out to connect with others with kindness, she says. When asked about what we can do when we meet unkind people, she says that kindness is a practice and it is hard. We need to keep in perspective that as humans, we do not have it altogether. Hurt people hurt others. Many people have histories of trauma and many people are in pain.
Dr Harding had in her article Why Kindness Is the Key to Improved Well-being also highlighted that studies have shown that the strongest predictor of a man's death from heart disease isn't cholesterol or blood pressure. It's his job. Or her job. Everyone knows it's important to have a good doctor, but it's also important to have a good manager and to give people the skills that they need to be good managers!
She calls on CEOs to look at the process and the people involved even while focusing on the bottom line, suggesting provocatively that they toss out their human [resources] manual and just rewrite it as, "Be kind." We need to be kind to people in our schools, in our workplaces and all of these different capacities.
Given that work takes up so much of our time and energies, business and school leaders and leaders of human resource who heed Dr Harding's call to write "Be Kind" in their human resource manuals and to give people the skills to be good managers can make a difference to the health and well-being of their workforce.
Josh Bersin, leading HR thinker, in his article Our New Role: Bringing Kindness to Work posits that the human element is most important of all and that a new role of HR leaders is to bring kindness to work. He says, "kindness at work has now become fundamental. While inclusion, fair pay, and development remain important, kindness and connection are now essential."
We need to redesign the workplace for kindness!
#Kindness #Well-being #Workplacehealth #Management #Schools #HumanResource
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beijing subway cost
Taking the Beijing subway is easy. The first train —— The last train —— Just swipe your Yikatong on the way in and the way out. This information is relative as of November 2019. The first train 5:10 The last train 22:55 SIHUI East—PINGGUOYUAN. Sanyuanqiao Subway Station Beijing Metro Map: Subway Lines. The Beijing Metro currently boasts 394 stations across 23 lines but this number is ever growing and will not stop anytime soon! The airport subway has only four stops: Dongzhimen, Sanyuanqiao, Terminal 2 and Terminal 3 of the Beijing … You can visit major tourist attractions in Beijing, please read our page The Complete Guide of Visiting Beijing by Subway. Beijing Subway: Cheap but crowded - See 1,731 traveler reviews, 756 candid photos, and great deals for Beijing, China, at Tripadvisor. Subway Fares from Daxing Airport. A handy Chinese app to have is the Explore Beijing Subway Map. The Beijing Subway switched from a fixed-fare to a distance-based fare schedule for all lines except the Capital Airport Express in 2014. Address: Dongzhimen, Dongcheng, Beijing, China, 100006 Dongzhimen Station is located on the northeastern 2nd Ring Road, about 8km to the city center Tian'anmen Square, 700m to Dongzhimen Long-distance Bus Station. Passengers can change to subway Line 2 and Line 13 from Express train here. Please check the official website to see first and last train time for each line and station. The Line 7 and Line 15 phase I Section 3 are expected to be commissioned by early 2014. Beijing Subway is planning to have 19 lines totalling 708km (440mi) of track in operation by 2015, and 1,050 km (650mi) of track by 2020, with an expected nine million passenger journeys a day. The cost of a single ride starts at 3 Yuan and increases with the distance. Visit Beijing by bus tours. The subway's first line opened in 1971, and the network now has 9 lines, 147 stations and 228 km of tracks in operation and delivers over 4 million rides per day. Beijing Airport Subway. With more than 200 stations built since its establishment in 1969, and with records of more than ten million passengers in one day, Beijing has taken over Moscow's as the world's second busiest subway in 2013, second only to the Seoul Metropolitan Subway.As a matter of fact, Beijing is getting even busier. While price of bus is lower than subway, if holding bus card you will get a 50% discount, for example, if you are studying in Peking University and wanting to go to the Palace Museum, taking subway would cost 5 yuan, while the cost by bus is 4 yuan (using bus card is 2 yuan), and if you take taxi need 47 yuan. On the other hand, a one-way business class metro ticket costs 50 RMB (6.3€ / 7$). Signs at the subway stations and in the trains as well as regular announcements for the next stop are in English and Chinese. Dongzhimen Subway Station. Visit Beijing by Subway. Beijing Subway Opening Time. Beijing subway [Photo via tuchong.com] As of December 2019, there were 23 lines operating in Beijing's rail transit network, with a total mileage of 699.3 kilometers and 405 stations (including 62 … The airport express of the Beijing Subway, known as ABC (short for Airport Beijing City), is one convenient transportation connecting both the Beijing airport and the center of the city. Beijing Subway ( or Beijing Metro) is a rapid transit rail network that serves the urban and suburban districts of Beijing municipality. Τhe ordinary one-way ticket costs 35 RMB (4.4€ / 4.8$) for an adult if the final subway station is Caoqiao Station and 25 RMB (3.1€ / 3.5$) if the alighting takes place at Daxing Xincheng Station. Beijing Subway - Beijing Metro.
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beijing subway cost 2020