Question

A sector of a circle has central angle 120 degrees and arc length 10π

centimeters. What is the radius of the circle

Answer 1

the radius = 15 cm

Explanation:

let r be the radius of the circle.

→ We know that in circle , the length of an arc

and the corresponding central angle are proportional.

180 corresponds to πr

120 corresponds to 10π

Then

`(\uppi r)/(180) =(10\uppi )/(120)`

`\Longrightarrow r=(180* 10\pi )/(120\pi ) =(180)/(12) =15`