Question #N942
A circle with center $O$ has radius 10. Points $A$ and $B$ lie on the circle, and the measure of central angle $AOB$ is 120 degrees. What is the area of sector $AOB$?
A. $\frac{100\pi}{3}$
B. $\frac{50\pi}{3}$
C. $100\pi$
D. $50\pi$
Correct Answer is: A
The area of a sector of a circle is given by the formula $\frac{\theta}{360} \pi r^2$, where $\theta$ is the measure of the central angle in degrees and r is the radius of the circle. In this case, $\theta = 120$ and $r = 10$, so the area of sector $AOB$ is $\frac{120}{360} \pi (10)^2 = \frac{100\pi}{3}$.