text: # Circular pool
  
  The base of the pool is a circle with a radius r = 10 m, excluding a circular segment that determines the chord length 10 meters. The pool depth is h = 2m. How many hectoliters of water can fit into the pool?
  
  Correct result:
  
  x =  6102 hl
  
  #### Solution:
  
  r=10 \ \text{m} \ \\ t=10 \ \text{m} \ \\ h=2 \ \text{m} \ \\ a=t/2=10/2=5 \ \text{m} \ \\ \ \\ α=2 \cdot \ \arcsin ( \dfrac{ a }{ r } )=2 \cdot \ \arcsin ( \dfrac{ 5 }{ 10 } ) \doteq 1.0472 \ \text{rad} \ \\ α_{2}=α \rightarrow ^\circ =α \cdot \ \dfrac{ 180 }{ \pi } ^\circ =1.0472 \cdot \ \dfrac{ 180 }{ \pi } ^\circ =60 ^\circ ^\circ \ \\ \ \\ S_{1}=\pi \cdot \ r^2 \cdot \ \dfrac{ 2 \pi - α }{ 2 \pi }=3.1416 \cdot \ 10^2 \cdot \ \dfrac{ 2 \cdot \ 3.1416 - 1.0472 }{ 2 \cdot \ 3.1416 } \doteq 261.7994 \ \text{m}^2 \ \\ \ \\ b=\sqrt{ r^2-a^2 }=\sqrt{ 10^2-5^2 }=5 \ \sqrt{ 3 } \ \text{m} \doteq 8.6603 \ \text{m} \ \\ \ \\ S_{2}=\dfrac{ a \cdot \ b }{ 2 }=\dfrac{ 5 \cdot \ 8.6603 }{ 2 } \doteq 21.6506 \ \text{m}^2 \ \\ \ \\ S=S_{1} + 2 \cdot \ S_{2}=261.7994 + 2 \cdot \ 21.6506 \doteq 305.1007 \ \text{m}^2 \ \\ \ \\ V=h \cdot \ S=2 \cdot \ 305.1007 \doteq 610.2013 \ \text{m}^3 \ \\ \ \\ x=V \rightarrow \ \text{hl}=V \cdot \ 10 \ \ \text{hl}=610.2013 \cdot \ 10 \ \ \text{hl}=6102 \ \text{hl}
  
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explanation: The document contains a math problem and its solution. The problem is about calculating the volume of a circular pool with a specific shape and converting the volume to hectoliters. The solution is provided, and the correct result is given as 6102 hectoliters.
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distilabel_metadata.content: # Circular pool
  
  The base of the pool is a circle with a radius r = 10 m, excluding a circular segment that determines the chord length 10 meters. The pool depth is h = 2m. How many hectoliters of water can fit into the pool?
  
  Correct result:
  
  x =  6102 hl
  
  #### Solution:
  
  r=10 \ \text{m} \ \\ t=10 \ \text{m} \ \\ h=2 \ \text{m} \ \\ a=t/2=10/2=5 \ \text{m} \ \\ \ \\ α=2 \cdot \ \arcsin ( \dfrac{ a }{ r } )=2 \cdot \ \arcsin ( \dfrac{ 5 }{ 10 } ) \doteq 1.0472 \ \text{rad} \ \\ α_{2}=α \rightarrow ^\circ =α \cdot \ \dfrac{ 180 }{ \pi } ^\circ =1.0472 \cdot \ \dfrac{ 180 }{ \pi } ^\circ =60 ^\circ ^\circ \ \\ \ \\ S_{1}=\pi \cdot \ r^2 \cdot \ \dfrac{ 2 \pi - α }{ 2 \pi }=3.1416 \cdot \ 10^2 \cdot \ \dfrac{ 2 \cdot \ 3.1416 - 1.0472 }{ 2 \cdot \ 3.1416 } \doteq 261.7994 \ \text{m}^2 \ \\ \ \\ b=\sqrt{ r^2-a^2 }=\sqrt{ 10^2-5^2 }=5 \ \sqrt{ 3 } \ \text{m} \doteq 8.6603 \ \text{m} \ \\ \ \\ S_{2}=\dfrac{ a \cdot \ b }{ 2 }=\dfrac{ 5 \cdot \ 8.6603 }{ 2 } \doteq 21.6506 \ \text{m}^2 \ \\ \ \\ S=S_{1} + 2 \cdot \ S_{2}=261.7994 + 2 \cdot \ 21.6506 \doteq 305.1007 \ \text{m}^2 \ \\ \ \\ V=h \cdot \ S=2 \cdot \ 305.1007 \doteq 610.2013 \ \text{m}^3 \ \\ \ \\ x=V \rightarrow \ \text{hl}=V \cdot \ 10 \ \ \text{hl}=610.2013 \cdot \ 10 \ \ \text{hl}=6102 \ \text{hl}
  
  We would be pleased if you find an error in the word problem, spelling mistakes, or inaccuracies and send it to us. Thank you!
  
  Tips to related online calculators
  Do you know the volume and unit volume, and want to convert volume units?
  
  #### You need to know the following knowledge to solve this word math problem:
  
  We encourage you to watch this tutorial video on this math problem:
  
  ## Next similar math problems:
  
  • Pascal's law
  Please calculate according to Pascal's law. Krupp's machines were known for their large size. In 1861, a blacksmith's steam hydraulic press was put into operation in Essen. What was the cross-sectional area of the larger piston if a compressive force of 1
  • Gears
  The front gear on the bike has 32 teeth and the rear, on the wheel, has 12 teeth. How many times does the rear wheel of the bike turns if you turn the right pedal 30 times? What distance will you go if the circumference of the bicycle wheel is 250 cm?
  • Sphere in cone
  A sphere is inscribed in the cone (the intersection of their boundaries consists of a circle and one point). The ratio of the surface of the ball and the contents of the base is 4: 3. A plane passing through the axis of a cone cuts the cone in an isoscele
  • Winch drum
  Originally an empty winch drum with a diameter of 20 cm and a width of 30 cm on the rescue car, he started winding a rope with a thickness of 1 cm beautifully from edge to edge. The winch stopped after 80 turns. It remains to spin 3.54m of rope (without h
  • Circular railway
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  • RPM
  An electric motor makes 3,000 revolutions per minutes. How many degrees does it rotate in one second?
  • Steel tube
  The steel tube has an inner diameter of 4 cm and an outer diameter of 4.8 cm. The density of the steel is 7800 kg/m3. Calculate its length if it weighs 15 kg.
  • Metal tube
  Calculate the metal tube mass 8dm long with the outer radius 5cm and the inner radius 4.5cm and 1cm3 of this metal is 9.5g.
  • The pot
  The pot is a cylinder with a volume of V = 7l and an inner diameter of d = 20cm. Find its depth.
  • Velocipedes
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  • Diameter of a cylinder
  The diameter of the cylinder is 42 cm. How many times does the cylinder turn on a 66m long track?
  • Cylinder height
  Calculate the height of the cylinder and its surface is 2500 dm2 and the bases have a diameter 5dm.
  • Collect rain water
  The garden water tank has a cylindrical shape with a diameter of 80 cm and a height of 12 dm. How many liters of water will fit into the tank?
  • Height as diameter of base
  The rotary cylinder has a height equal to the base diameter and the surface of 471 cm2. Calculate the volume of a cylinder.
  • Special watch
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  • Perimeter of base
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distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document contains a math problem and its solution. The problem is about calculating the volume of a circular pool with a specific shape and converting the volume to hectoliters. The solution is provided, and the correct result is given as 6102 hectoliters.
  
  Label: question-and-answer