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Lesson 11-2
Surface Areas of Prisms and Cylinders
Lesson Objectives
1 Find the surface area of a prism
2 Find the surface area of a cylinder
NAEP 2005 Strand: Measurement
Topic: Measuring Physical Attributes
Local Standards: ____________________________________
Vocabulary and Key Concepts.
Theorem 11-1: Lateral and Surface Area of a Prism
and the
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The lateral area of a right prism is the product of the
.
L.A. ph
The surface area of a right prism is the sum of the
the
and
.
S. A. L.A. 2B
c
d
c
d
a bh
a
c
d
h
d
Lateral Area ph
b
c
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Perimeter of base
abcd
a b c d
h
Surface Area L.A. 2B
Theorem 11-2: Lateral and Surface Area of a Cylinder
The lateral area of a right cylinder is the product of the
and the
.
L.A. 2πrh, or L.A. πdh
The surface area of a right cylinder is the sum of the
and the
.
S.A. L.A. 2B, or S.A. 2πrh h
h
2πr
208
2πr 2
Geometry Lesson 11-2
Area
Area
r
r
Area of a base
B
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A prism is
prism
The bases of a polyhedron are
Lateral faces are
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An altitude is
The height is
Bases
The lateral area of a prism is
prism
The surface area of a prism or a cylinder is
h
h
A right prism is
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prisms
h
An oblique prism is
prism
h
A cylinder is
In a cylinder, the bases are
h
cylinders
The lateral area of a cylinder is
A right cylinder is
An oblique cylinder is
h
cylinder
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Geometry Lesson 11-2
209
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Examples.
1 Using Formulas to Find Surface Area Find the surface area of a 10-cmhigh right prism with triangular bases having 18-cm edges. Round to the
nearest whole number.
Use the formula
to find the lateral area and
the formula
to find the surface area of the
prism. The area B of the base is 12 ap, where a is the apothem and p is the
.
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cm.
cm
18
18
cm
The triangle has sides of length 18 cm, so p 3 ? 18 cm, or
Use the diagram of the base.
60 a
Use 30°-60°-90° triangles to find the
30
9 cm
9 cm
!3 ? shorter leg longer leg
a
9
a
9
Divide both sides by
?
.
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9
?
.
Rationalize the denominator.
B 5 12ap
B 12 ?
?
Substitute
B
for a and
Simplify.
The area of each base of the prism is
S.A. 5 L.A. 1 2B
2B
(
)(
cm2.
Use the formula for surface area.
Substitute
) 2(
<
) Substitute
Geometry Lesson 11-2
for L.A.
for p,
for h and
for B.
Simplify.
Use a calculator.
Rounded to the nearest whole number, the surface area is
210
for p.
.
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2 Finding Surface Area of Cylinders A company sells cornmeal and barley
in cylindrical containers. The diameter of the base of the 6-in.-high cornmeal
container is 4 in. The diameter of the base of the 4-in.-high barley container
is 6 in. Which container has the greater surface area?
Find the surface area of each container. Remember that r d2.
Cornmeal Container
S.A. 5
Barley Container
1
Use the formula for surface area.
Substitute the formulas for lateral
area of a cylinder and area of a circle.
5 2prh 1
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2π
( )( ) 2π (
5
S.A. 5
2
)
1
5
Because 42π in.2
surface area.
32π in.2, the
Substitute for r and h.
1
2pr2
5
2π
Simplify.
5
Combine like terms.
5
( )( ) 2π (
)
2
1
container has the greater
Quick Check.
1. Use formulas to find the lateral area and surface area of the prism.
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6m
12 m
2. Find the surface area of a cylinder with height 10 cm and radius 10 cm in
terms of π.
3. The company in Example 2 wants to make a label to cover the cornmeal
container. The label will cover the container all the way around, but will not
cover any part of the top or bottom. What is the area of the label to the
nearest tenth of a square inch?
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Geometry Lesson 11-2
211