Download 11-3 - Ithaca Public Schools

Name
Class
Date
Enrichment 11-3
Frustum of a Solid
A frustum of a pyramid or cone is the figure created when the tip of the
pyramid or cone is cut off 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.
b
h
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The figure at the upper right is a frustum of a regular 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.
a
r
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.
h
Use the frustum of the regular square pyramid above to derive a surface
area formula.
R
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?
6. What is the formula for the surface area of a frustum of a regular
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.
11.
4 cm
4 in.
12.
13.
14.
9 ft
6 cm
12 m
18 m
15 in.
8 ft
10 ft
6 cm
7 in.
Geometry Chapter 11
22 m
5 cm
11 in.
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5. What is the lateral area of the figure?
20
m
12 ft
Lesson 11-3 Enrichment
17