1. 11.1 Arc Length

2. REVIEW: RADIUS, DIAMETER & CIRCUMFERENCE
The radius, r, is the measure of the distance from the center to the side of a circle.
The diameter, d, is the measure of a chord that passes through the center of a circle.
Circumference, C, is the distance around the circle.
If you unwrap a circle, how long will the line be? or
𝐶=2𝜋𝑟

3. Example: Find the Circumference of the Circle
Exact Answer cm cm
Approximate Answer

4. Fraction of a Circle
What fraction of the whole circle is the given arc?
Find the measure of the arc.
Divide by 360, the total number of degrees in the circle.
180º
diameter

5. Arc Length The distance around an arc The ratio of the arc and 360°
The amount of crust on a slice of pizza.
The ratio of the arc and 360°
(the fraction of the circle) multiplied by the circumference.

6. Arc Length Formula = x 2r
Arc Length = (fraction of the circle) X (circumference)
= x 2r
= x 2r

7. Example: Find the Arc Length
A.L. (arc length) = fraction *circumference
A. L. =

8. Examples:
Find the length ) circumference ) radius of
of 𝑃𝑄 of ⨀𝑁 ⨀G

9. More examples:
The dimensions of a car tire are shown. To the nearest foot, how far does the tire travel when it makes 15 revolutions?
Step 1: Find the diameter of the tire.
D =
= 26 in.
Step 2: Find the circumference of the tire.
C = πd
= 26 π in.
Step 3: Find the distance traveled in 15 revolutions.
(1 revolution = distance of the circumference)
Distance traveled = # revolutions * Circumference
= 15 * 26 π
= 390 π in.
= in.
in ÷12 in/ft = 102 ft.

10. And more examples: Find the perimeter of the shaded region. a) b)