18.2/3 Pyramids - right, oblique - Cavalieri's Principle

1. Move the apex points laterally. How are the areas of the base and cross sections affected? How is the volume of each pyramid affected?

2. Vary the height. 3. Vary the height of the cross sections. How would you compare the three cross sections as you change the height?

4. Vary the shape of the base of the third figure. How does the shape of the base affect the scaling of the cross sections? How does it affect the volume of the pyramids?

5. Approximate the shape of a circle with the base of the third figure as best you can. Vary the height, the height of the cross sections, and the position of the apex points. What conjecture can you make about the volume of a cone?