11.1 Arc Length

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

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

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

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.

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

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

Examples: Find the length 2) circumference 3) radius of of 𝑃𝑄 of ⨀𝑁 ⨀G

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 = 5.5 + 15 + 5.5 = 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. = 1225.2 in. 1225.2 in ÷12 in/ft = 102 ft.

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