# Building a Volume Formula for a Pyramid

ID: rohoj-jutoh
Illustrative Mathematics, CC BY 4.0
Subject: Geometry
Standards: HSG-GMD.A.1HSG-GMD.B.4

7 questions

# Building a Volume Formula for a Pyramid

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##### 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.

1)

2)

##### 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 ﻿$k = 0.5$﻿.

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 ﻿$k$﻿. 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.