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

Answer: Radius of the circle = 72 units.

Step-by-step explanation:

Since we have given that

Length of an arc = 48π

Central angle = 120⁰

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

$L=\frac{\theta}{360}\times 2\pi r\\\\48\pi=\frac{120}{360}\times 2\times \pi\times r\\\\48=\frac{1}{3}\times 2\times r\\\\\frac{48\times 3}{2}=r\\\\24\times 3=r\\\\72\ units=r$

Hence, radius of the circle = 72 units.

Answer 2

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