Building a Volume Formula for a Pyramid
Cover Your Bases
For each solid, draw and label a prism or cylinder that has a base congruent to the solid’s and a height equal to the solid’s.
Comparing Cross Sections
Each solid in the image has height 6 units. The area of each solid’s base is 10 square units. A cross section has been created in each by dilating the base using the apex as a center with scale factor .
3) Calculate the area of each of the 3 cross sections.
4) Suppose a new cross section was created in each solid, all at the same height, using some scale factor . What would the area of each cross section be?
5) Explain your reasoning.
6) What does this information about cross sections tell you about the volumes of the 3 solids?
7) Calculate the volume of each of the solids.