Question

A circle has a radius of 48 millimeters. What is the central angle in radians, that intercepts an arc of length 36π millimeters?

Answer 1

arc length= radius x angle
36pie=48 x angle
divide both side by 48
you get 3/4pie

Answer 2

`\theta=(3\pi)/(4)`

Explanation:

The formula for length of intercepted arc is

`s=r\theta`

where, r is the radius of the circle and θ in the central angle in radian.

Radius of the circle = 48 millimeters

Length of intercepted arc = 36π millimeters

Substitute the given values in the above formula.

`36\pi=48\theta`

Divide both sides by 48.

`(36\pi)/(48)=(48\theta)/(48)`

`(3\pi)/(4)=\theta`

Therefore, the measure of central angle is
`\theta=(3\pi)/(4)`.