1. NOTES 10.9
Circumference and Arc Lengths

2. You should already know….
The circumference of a circle is its perimeter.
C = πd or C = 2πr
Leave answer in terms of π.
Only use a calculator when asked to approximate.

3. Length of an arc
The 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.

4. Given: circle O, arc AB = 40º, radius = 9 Find the length of arc AB.
Remember: Length of arc = (m arc) πd
360
Length of arc AB = 40 (πd)
= 1(18π)
= 2π

5. 1. Given: Circle O’s circumference is 64π inches
1. Given: Circle O’s circumference is 64π inches. Find the radius of circle O. O
C = πd
64π = πd
64 = d
32 in = r
2. Find the length of the arc of a circle with a 12-cm radius and 85º arc.
Length of arc = 85(24π)
= 𝟏𝟕𝝅 𝟑 cm

6. The diameter of a bicycle wheel (including the tire) is 70 cm.
How far will the bicycle travel if the wheel rotates 1000 times?
How many revolutions will the wheel make if the bicycle travels 15 m?
The distance covered in one revolution is equal to the circumference of the wheel. Thus, the bicycle travels 70π or 220 centimeters per revolution.
Distance = 1000(70π)
=70,000π cm
Or about 220,000 cm
The bicycle travels approximately 2.2m per revolution.
15 = 2.2x
6.8 = x
The wheel will revolve approximately 6.8 times.