Question

A circle has an arc of length 48π that is intercepted by a central angle of 120°. What is the radius of the circle?

Answer 1

arc length = circumference • (central angle (degrees) ÷ 360)
radius * 2 * PI = arc length / (central angle (degrees) ÷ 360)
radius = [arc length / (central angle (degrees) ÷ 360)] / 2*PI
radius = [48*PI / 120/360] / 2*PI
radius = 72

Answer 2

Answer: Radius of the circle = 72 units.

Explanation:

Since we have given that

Length of an arc = 48π

Central angle = 120⁰

As we know the formula for " length of an arc"

`L=(\theta)/(360)* 2\pi r\\\\48\pi=(120)/(360)* 2* \pi* r\\\\48=(1)/(3)* 2* r\\\\(48* 3)/(2)=r\\\\24* 3=r\\\\72\ units=r`

Hence, radius of the circle = 72 units.