Question #N814
A circle with center $O$ has a radius of 10. Point $A$ lies on the circle, and the measure of central angle $\angle AOB$ is $60^\circ$. What is the area of sector $AOB$?
A. $10 \pi$
B. $20 \pi$
C. $\frac{50}{3} \pi$
D. $\frac{100}{3} \pi$
Correct Answer is: D
The area of a sector is a fraction of the area of the whole circle, equal to the measure of the central angle divided by 360 degrees. In this case, the area of sector $AOB$ is $\frac{60^\circ}{360^\circ} = \frac{1}{6}$ of the area of the whole circle. The area of the whole circle is $\pi r^2 = \pi (10)^2 = 100 \pi$, so the area of sector $AOB$ is $\frac{1}{6} \cdot 100 \pi = \frac{100}{3} \pi$.