Circumference and Arc Lengths

Lesson 10.9

The circumference of a circle is its perimeter.

C = πd

Leave answer in terms of π unless asked to approximate. Then use a calculator.

Things you should already know about circumference…

Length of an arcThe length of an arc depends on the

circumference of the circle and the measure of the arc.

Theorem 98: The length of an arc is equal to the circumference of its circle times the fractional part of the circle determined by the arc.

A

B

Given: circle O, arc AB = 40º, radius = 3

Find the length of arc AB.O

Remember: Length of arc = (m arc) πd360

OR arc length = arc measurecircumference 360

Length of arc AB = 40 (Circumference) 360 = 1(36π) 9 = 4π

1. Given: Circle O’s circumference is 64π inches. Find the radius of circle O.

O

2. Find the length of the arc of a circle with a 12-cm radius and 105º arc.

C = πd64π = πd64 = d32 in = r

Length of arc = 105(24π) 360 = 7π cm

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?

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

a. The distance covered in one revolution is equal to the circumference of the wheel. Thus, the bicycle travels 70π or 220 centimeters per revolution.a. Distance = 1000(70π)b. =70,000π cmc. Or about 220,000 cm

b. The bicycle travels approximately 2.2m per revolution.a. 15 = 2.2xb. 6.8 = xc. The wheel will revolve approximately 6.8 times.