Question

Suppose that circles R and S have a central angle measuring 60°. Additionally, the length of the intercepted arc for circle R is 10 3 π meters and for circle S is 16 3 π 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

It should be 16 meters.

Answer 2

D) 16 meters

Explanation:

Givens

The lenght of the intercepted arc of R is
`103\pi \ m`.

The length of the intercepted arc of S is
`163 \pi \ m`.

The radius of circle R is
`10 \ m`.

With these arcs, we can elaborate the following proportion between radius and arcs:

`(r_(S) )/(r_(R) ) =(arc(S))/(arc(R))`

Replacing values, we have

`(r_(S) )/(10)=(163\pi)/(103 \pi) \\r_(S)=(1630)/(103) \approx 16 \ m`

Therefore, the right answer is D.