Question

A circle has a radius of 20 inches. Find the length of the arc intercepted by a central angle of 45°. Leave answers in terms of π .

Answer 1

Explanation:

the length of the full circle arc of 360° (also called circumference) is

2pi×r

r being the radius.

so, if we have only a fraction of the full circumference defined by the same fraction of 360° via the given angle, we then know that the length of that arc is

2pi×r × angle/360

in our case we have

2pi × 20 × 45/360 = 2pi × 20 × 1/8 = pi×20×1/4 = 5pi

the length of the arc is 5pi inches.