Chapter 12-2 Lesson: Surface Areas of Prisms and Cylinders
The lateral area is 240 square centimeters, and the surface area is 384 square centimeters.
Exercises
Find the lateral area and surface area of each regular pyramid. Round to the nearest tenth if necessary.
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(continued)
Chapter 12-2 Lesson: Surface Areas of Prisms and Cylinders
Lateral and Surface Areas of Cylinders A cylinder is a solid with bases that are
congruent circles lying in parallel planes. The axis of a cylinder is the segment with
endpoints at the centers of these circles. For a right cylinder, the axis is also the altitude
of the cylinder.
Lateral Area
of a Cylinder
If a cylinder has a lateral area of L square units, a height of h units, and a base
has a radius of r units, then L = 2πrh.
Surface Area
of a Cylinder
If a cylinder has a surface area of S square units, a height of h units, and a
base has a radius of r units, then S = L + 2B or 2πrh + 2πr2.
Example: Find the lateral and surface area of the cylinder. Round to the nearest tenth.
If d = 12 cm, then r = 6 cm.
L = 2πrh
= 2π(6)(14)
≈ 527.8
S = 2πrh + 2𝜋𝑟 2
Lateral area of a cylinder
r = 6, h = 14
Use a calculator.
Surface area of a cylinder
≈ 527.8 + 2𝜋 (6)2
2πrh ≈ 527.8, r = 6
≈ 754.0
Use a calculator.
The lateral area is about 527.8 square centimeters and the surface area is about 754.0 square centimeters.
Exercises
Find the lateral area and surface area of each cylinder. Round to the nearest tenth.
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Chapter 12-3 Practice Surface Areas of Prisms and Cylinders
ANSWER KEY TO LESSON 12-2
Part I
Part II
Additional Practice