Name: __________________________
Geometry Lesson 103
Date: ________________________
Objective: TSW use frustums of cones and pyramids.
Period: ______________________
If the top of a cone or a pyramid is removed, eliminating the figure’s vertex, the result is a
frustum.
A frustum of a cone is a part of a cone with two parallel circular bases.
A frustum of a pyramid is a part of a pyramid with two parallel bases.
Volume of a Frustum - The following formula is used to find the volume of a
frustum, regardless of whether it is part of a cone or a pyramid. The variables
𝐵1 and 𝐵2 are the areas of the two bases and h is the height of the frustum.
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Example 1 Finding the Volume of a Frustum of a Pyramid
Find the volume of the frustum of the pyramid shown.
SOLUTION
Example 2 Finding the Volume of a Frustum of a Cone
a. Find the volume of the frustum of the cone to the nearest hundredth of a cubic inch.
SOLUTION
Geometry Lesson 103
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b. Find the areas of the frustum’s bases.
SOLUTION
Example 3 Application: Farming
A grain silo is shaped like a cone, as shown in the diagram. If the height
of the grain in the silo is 40 feet, what volume of grain is in the silo, to
the nearest cubic foot?
SOLUTION
You Try!!!!
a. Find the volume of this frustum of a pyramid. Round your answer to the nearest
cubic inch.
Geometry Lesson 103
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b. Find the volume of this frustum of a cone to the nearest hundredth.
c. The Great Pyramid of Giza is the largest of ancient Egypt’s pyramids. It is a
square pyramid that stands 147 meters tall. The diagram depicts what the Great
Pyramid might have looked like during construction. Given the dimensions in the
diagram, what is the volume of the pyramid at this point in its construction?
Geometry Lesson 103