Basic Mathematics for College Students

If we multiply both sides of pCDby , we have the following formula.D

794 Chapter 9 An Introduction to Geometry

Circumference of a Circle

The circumference of a circle is given by the formula

CpD where is the circumference and C Dis the length of the diameter

Since a diameter of a circle is twice as long as a radius , we can substitute for

in the formula to obtain another formula for the circumference :

C 2 pr The notation 2 prmeans 2 pr.

D CpD C

r 2 r

EXAMPLE (^1) Find the circumference of the
circle shown on the right. Give the exact answer and
an approximation.
StrategyWe will substitute 5 for in the formula
and evaluate the right side.
WHYThe variable represents the unknown
circumference of the circle.
Solution
This is the formula for the circumference of a circle.
Substitute 5 for r,the radius.
When a product involves P, we usually rewrite it so that Pis
the last factor.
Do the first multiplication: 2(5) 10. This is the exact answer.
The circumference of the circle is exactly cm. If we replace with 3.14, we get
an approximation of the circumference.
To multiply by 10, move the decimal point in 3.14 one place to the right.
The circumference of the circle is approximately 31.4 cm.

C31.4

C10(3.14)

C 10 P

10 p p

C 10 p

C2(5)p

C 2 p( 5 )

C 2 pr

C

C 2 pr

r

Self Check 1

Find the circumference of

the circle shown below. Give

the exact answer and an

approximation.

Now TryProblem 25

12 m

5 cm

Using Your CALCULATOR Calculating Revolutions of a Tire

When the key on a scientific

calculator is pressed (on some models,

the key must be pressed first), an

approximation of is displayed. To

illustrate how to use this key, consider

the following problem. How many times

does the tire shown to the right revolve

when a car makes a 25-mile trip?

We first find the circumference of the tire. From the figure, we see that the

diameter of the tire is 15 inches. Since the circumference of a circle is the

product of and the length of its diameter, the tire’s circumference is

inches, or inches. (Normally, we rewrite a product such as so that

is the second factor.)

15 p p 15 p

p p 15

p

2nd

p

15 in.

One revolution