Find the length of the arc on a circle of radius r intercepted by a central angle θ. (Round your answer to two decimal places.) Radius r Central Angle θ 16 inches 240°

Question

Find the length of the arc on a circle of radius r intercepted by a central angle θ. (Round your answer to two decimal places.)

Radius r		Central Angle θ
16 inches		240°

Answer 1

A circle has circumference 2pi(r)

240 degrees is 240/360 of a circle or 24/36 = 6/9 = 2/3 of the circle

the arc is 2/3 of 2pi(r) = 2/3 x 2pi x 16 inches

General formula for the length of an arc is

Arc Length = theta times radius, with theta in radians 240 degrees = 4pi/3 radians

Arc = 4pi/3 x 16 = 64pi/3

= about 67.02 inches

pi/3 is slightly more than 1

64 times slightly more than 1 is slightly more than 64.