Question

A circle has an arc of length 56 pie that is intercepted by a central angle of 120°.

What is the radius of the circle?

Answer 1

120° = 2π/3 radians

radius = 56π/(2/3π) = 84 units

answer: 84 units

Explanation:

Answer 2

Therefore radius is 84 units.

Explanation:

Given:

arc length = 56 pie

Central angle = θ = 120°

pi = 3.14

To Find:

Radius = r =?

Solution:

If the θ measured in degree then the arc length is given as

`\textrm{arc length}=(\theta)/(360\°)* 2\pi r`

Where r = radius, θ = Central angle

On substituting the values we get

`56\pi=(120)/(360)* 2\pi* r\\\\r=(3* 56)/(2)=84\\\therefore r=84\ unit`

Therefore radius is 84 units.