Answer: D

Let the central angle be $\theta$ degrees. The arc length is $\frac{\theta}{360}(2\pi r) = 5\pi$, and the area is $\frac{\theta}{360}(\pi r^2) = 15\pi$. Dividing the area equation by the arc length equation gives $\frac{r}{2} = \frac{15\pi}{5\pi} = 3$, so $r = 6$.

Choice B is the ratio $\frac{15\pi}{5\pi} = 3$, but that ratio equals $\frac{r}{2}$, not $r$.

Why the other choices are wrong

• A. This treats 5π as the circumference of the whole circle.
• B. The area divided by the arc length is half the radius, so 3 is r/2, not r.
• C. This treats 15π as the area of the whole circle.