Page 14 - Math Course 2 (Book 2)

Geometric Surface Area: Cylinders

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L = 2πrh Lateral area of a cylinder 0 = r + 10r – 264 Subtract 264 from each side.
0 = (r + 22)(r – 12) Factor.
= 2π(3.15)(12) r = 3.15, h = 12
r = –22 or 12 Solve.
≈ 237.5 Use a calculator.

About 237.5 square centimeters Since a radius of a circle cannot have a negative
Answer of aluminum are used to make value, –22 is eliminated.
the sides of the can.
The radius of the base is 12
Answer
feet.
Surface Area of a Cylinder

Example Your Turn!

Find the surface area of the cylinder. Real World Example

14 ft A set of toy blocks is sold in a cylindrically shaped
container. A product label wraps around all sides
The radius of the base and of the container without any overlaps or gaps. How
the height of the cylinder much paper is used to make the label the
18 ft are given. Substitute these appropriate size if the diameter of the container is
values in the formula to find 12 inches and the height is 18 inches? Round to the
the surface area. nearest tenth.

L = 2πrh + 2π 2 Surface area of a cylinder A. 1357 in 2
B. 678.6 in 2
= 2π(14)(18)+ 2π(14) 2 r = 14, h = 18 C. 339.3 in 2
D. 432 in 2
≈ 2814.9 Use a calculator.

The surface area is approximately
Answer Answer
2814.9 square feet.

Surface Area of a Cylinder

Find Missing Dimensions Find the surface area of the cylinder to the nearest
tenth.
Example A. 1156.1 ft 2

B. 955.0 ft 2
Find the radius of the base of a right cylinder if the C. 578.1 ft 2
surface area is 528π square feet and the height is 2
10 feet. D. 3015.9 ft

Use the formula for surface area to write and solve
an equation for the radius.
T = 2πrh + 2πr 2 Surface area of a cylinder

528π = 2π(10)r + 2πr 2 Substitution
528π = 20π + 2πr 2 Simplify.
Answer
260 = 10r + r 2 Divide each side by 2π
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