10.9 Circumference and Arc Length

After studying this section, you will be able to determine the circumference of a circle and the

length of an arc.

Circumference

Postulate or 2C d C r

Example 1

Find, to the nearest hundredth, the circumference of a circle whose radius is 5.37 in.

Definition The circumference of a circle is its perimeter

Length of an Arc

Example 2

Find the length of a 40 arc of a circle with an 18 cm radius.

Arc length is a linear measurement. The length of an arc depends both on the arc’s measure and on the

circumference of its circle.

Theorem The length of an arc is equal to the circumference of its circle times the fractional part of the circle determined by the arc

PQ

length of PQ 2360

mr

where r is the radius and is measured in degrees.PQ

Example 3

Find the radius of a circle whose circumference is 50

Example 4

Find the length of each arc of a circle with a 12 cm radius.

a.A 30 arc

b.A 105 arc

Example 5

The diameter of a bicycle wheel (including the tire) is 70 cm.

a.How far will the bicycle travel if the wheel rotates 1000 times? (to the nearest meter)

b.How many covered revolutions will the wheel make if the bicycle travels 15 m.

Summary

How can circumference be used in everyday life?

Homework:

Worksheet 10.9