1. Frustums of Cones and Pyramids
Lesson 103
Frustums of Cones and Pyramids

2. What is a frustum?
If the top of a cone or pyramid is removed, then the result is a frustum with parallel bases. What would the vertical cross-section of these shapes be?

3. Volume of a Frustum
Regardless if the frustum is part of a cone or a pyramid 𝑉= 1 3 ℎ 𝐵 1 + 𝐵 1 𝐵 2 + 𝐵 2 where B1 and B2 are the area of the bases and h is the height of the frustum.

4. Find the volume of the frustum Units are in meters
𝑉= 1 3 ℎ 𝐵 1 + 𝐵 1 𝐵 2 + 𝐵 2 𝑉= 1 3 ∙ 𝑉= 𝑉= 𝑉=56 𝑚 3

5. Find the exact volume
𝑉= 1 3 ℎ 𝐵 1 + 𝐵 1 𝐵 2 + 𝐵 2 𝑉= 1 3 ∙30 100𝜋 𝜋 20 2 𝜋 +400𝜋 𝑉=10 500𝜋+10∙20∙𝜋 𝑉=10 500𝜋+200𝜋 𝑉=10 700𝜋 𝑉=7000𝜋 𝑐𝑚 3

6. What is the volume of this container?
𝐵 1 = 𝐵 2 =8 12
𝐵 1 = 𝐵 2 =96
𝑉= ∙ 𝑉=
𝑉=217 𝑖𝑛 3

7. Questions?