Unit 5, Lesson 13

Building a Volume Formula for a Pyramid

Geometry

Practice

Problem 1

Find the volume of a pyramid whose base is a square with side lengths of 6 units and height of 8 units.

Problem 2

A cylinder has radius 9 inches and height 15 inches. A cone has the same radius and height.

Find the volume of the cylinder.
Find the volume of the cone.
What fraction of the cylinder’s volume is the cone’s volume?

Problem 3

Each solid in the image has a height of 4 units. The area of each solid’s base is 8 square units. A cross-section has been created in each by dilating the base using the apex as a center with a scale factor of \(k=0.25\).

<p>A pyramid with a triangular base. Another pyramid with a rectangle base.</p>

Calculate the area of each of the 2 cross-sections.
Suppose a new cross-section was created in each solid, both at the same height, using some scale factor \(k\). How would the areas of these 2 cross-sections compare? Explain your reasoning.

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Building a Volume Formula for a Pyramid

Practice

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8