Volume of Pyramids and Cones

Use the sliders on the left side of the GeoGebra file to manipulate different characteristics of the prism, pyramid, cylinder, and cone. PSide: Adjusts the side length of the base of the prism and pyramid. PHeight: Adjusts the height of the prism and pyramid. CRadius: Adjusts the radius of the base of the cylinder and cone. CHeight: Adjusts the height of the cylinder and cone. Do you notice any relationships between any of the figures?
Discuss the following questions with a partner or small group: 1. What were some things that you noticed while manipulating the figures in the GeoGebra file? 2. Can you use the GeoGebra file to create a formula that can be used to calculate the volume of a pyramid? 3. Can you use the GeoGebra file to create a formula that can be used to calculate the volume of a cone? 4. Does the GeoGebra file support your findings? Why or why not? Prepare an argument for your findings using mathematical language. 5. Can your findings be applied to all pyramids and cones? Why or why not? How do you know? 6. What out-of-school situations could you apply your findings to? Think of 3-4 examples per group.