Question

Suppose that circles R and S have a central angle measuring 60°. Additionally, the length of the intercepted arc for circle R is 103π meters and for circle S is 163π meters.
If the radius of circle R is 10 meters, what is the radius of circle S? A) 9 meters B) 12 meters C) 14 meters D) 16 meters

Answer 1

Cianna Ithink its 14 meters

Answer 2

The length of the intercepted arc for circle R = 103π meters

The length of the arc of circle S = 163π meters.

the radius of circle R = 10 meters

the radius of circle S = x

Given : circles R and S have a central angle measuring 60°

So the radius of circle S to the radius of circle R is equal to the length of intercepted arc S to the length of the arc R

$\frac{Radius S}{Radius R} = \frac{Length S}{Length R}$

$\frac{Radius S}{10} = \frac{163\pi }{103\pi }$

$Radius S = \frac{163\pi }{103\pi } * 10$

S= 15.825 meters

So the radius of the circle S = 16 meters