Another important solid shape that is not polyhedral is the cone. Open the GeoGebra file ctcoregeomACT622. Use the sliders to change the radius and height of the cone. Notice how the sliders affect right triangle at the left of the screen as well ABC as the circular base and sector used to form the lateral surface. cone’s How is the circular base related to the triangle? How is the sector for the lateral surface related to the triangle? How is the radian measure of the central angle related to the triangle? How can you make the sector cover almost its entire circle? How can you make the sector cover only a small fraction of its circle? Find an empty can with a missing lid. Work with a partner to try to make a paper cone that will fit exactly inside this can as in this picture. a. The net below shows the base and the lateral surface. How is the arc length of the sector related to the circumference of the base? Explain. b. How would you find the radius of the sector that forms the lateral surface? c. How would you find central angle for the sector? d. Show the calculations you and your partner made to create the cone that fits exactly inside the can.
Another important solid shape that is not polyhedral is the cone. Open the GeoGebra file ctcoregeomACT622. Use the sliders to change the radius and height of the cone. Notice how the sliders affect right triangle ABC at the left of the screen as well as the circular base and sector used to form the cone’s lateral surface. How is the circular base related to the triangle? How is the sector for the lateral surface related to the triangle? How is the radian measure of the central angle related to the triangle? How can you make the sector cover almost its entire circle? How can you make the sector cover only a small fraction of its circle? Find an empty can with a missing lid. Work with a partner to try to make a paper cone that will fit exactly inside this can as in this picture. a. The net below shows the base and the lateral surface. How is the arc length of the sector related to the circumference of the base? Explain. b. How would you find the radius of the sector that forms the lateral surface? c. How would you find central angle for the sector? d. Show the calculations you and your partner made to create the cone that fits exactly inside the can.
Activity_6_2_2.docx