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

Answer:

D) 16 meters

Step-by-step 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:

$\frac{r_{S} }{r_{R} } =\frac{arc(S)}{arc(R)}$

Replacing values, we have

$\frac{r_{S} }{10}=\frac{163\pi}{103 \pi} \\r_{S}=\frac{1630}{103} \approx 16 \ m$

Therefore, the right answer is D.