Page 667 - Basic College Mathematics with Early Integers

644 C HAPTE R 9 I GEOMETRY

To better understand circumference and p1pi2, let’s review the following
experiment.Take any can and measure its circumference and its diameter.

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1 2 3 4 5 6 7 8 9

The can in the figure above has a circumference of 23.5 centimeters and a diam-
eter of 7.5 centimeters. Now divide the circumference by the diameter.
circumference 23.5 cm
= L 3.13
diameter 7.5 cm
Try this with other sizes of cylinders and circles—you should always get a number
close to 3.1. The exact ratio of circumference to diameter is p. (Recall that
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p L 3.14 or L ) .
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PRACTICE 8 Example 8 Finding Circumference of Spa
a. An irrigation device waters a
Mary Catherine Dooley plans to install a border of new tiling around the circumfer-
circular region with a diame-
ence of her circular spa.If her spa has a diameter of 14 feet,find its exact circumference.
ter of 20 yards. Find the exact
Then use the approximation 3.14 for to approximate the circumference.p
circumference of the watered
region, then use p L 3.14 to
give an approximation.
14 feet

20 yd

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Solution: Because we are given the diameter, we use the formula C = p d.
C = pd
b. A manufacturer of clocks is
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designing a new model.To = p 14 ft Replace d with 14 feet.
help the designer calculate = 14p ft
the cost of materials to make
the new clock, calculate the The circumference of the spa is exactly 14p feet. By replacing p with the
circumference of a clock approximation 3.14, we find that the circumference is approximately
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with a face diameter of 14 feet 3.14 = 43.96 feet.
12 inches. Give an exact
circumference; then use Work Practice 8
p L 3.14 to approximate.

Answers
Concept Check The distance around which figure is greater: a square with
8. a. exactly 20p yd L 62.8 yd side length 5 inches or a circle with radius 3 inches? Copyright 2012 Pearson Education, Inc.
b. exactly 12p in. L 37.68 in.

Concept Check Answer
a square with side length 5 in.