Question #N450
A circle with center $O$ has radius 5. Points $A$ and $B$ lie on the circle such that the measure of minor arc $AB$ is $60^\circ$. What is the area of sector $AOB$?
A. $\frac{25\pi}{6}$
B. $\frac{25\pi}{3}$
C. $\frac{125\pi}{6}$
D. $\frac{125\pi}{3}$
Correct Answer is: A
The area of a sector is proportional to the measure of its central angle. Since the measure of minor arc AB is 60 degrees, the area of sector AOB is \frac{60}{360} = \frac{1}{6}$ the area of the circle. The area of the circle is $\pi r^2 = \pi (5)^2 = 25\pi$, so the area of sector AOB is \frac{1}{6} (25\pi) = \frac{25\pi}{6}$.