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11-3
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Date
Enrichment
Surface Areas of Pyramids and Cones
Frustum of a Solid
A frustum of a pyramid or cone is the figure made when the tip of the
pyramid or cone is cut of by a cross section that is perpendicular to the
height. In a frustum of a pyramid or cone, there are two bases, an upper
base and a lower base.
The figure at the upper right is a frustum of a square pyramid for which h
is the height, a is the length of a side of the lower base, b is the length of a
side of the upper base, and ℓ is the slant height.
The figure at the lower right is a frustum of a cone for which h is the
height, R is the radius of the lower base, r is the radius of the upper base,
and ℓ is the slant height.
Use the frustum of the regular square pyramid above to derive a surface area
formula.
1. What is the area of its lower base?
2. What is the area of its upper base?
3. What is the shape of each lateral face?
4. What is the area of each lateral face?
5. What is the lateral area of the figure?
6. What is the formula for the surface area of a frustum of a square pyramid?
Use the frustum of the cone above to derive a surface area formula.
7. What is the area of its lower base?
8. What is the area of its upper base?
9. What is the lateral area of the figure? (Hint: Consider the formula for the
lateral area of a cone.)
10. What is the formula for the surface area of a frustum of a cone?
Find the surface area of each figure below. Round your answers to the nearest tenth.
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Prentice Hall Geometry • Teaching Resources
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