Question

A chord $AB$ of a circle with center $O$ subtends an angle of ${120}^{\circ }$ at the center. If the radius of the circle is $30cm,$ find the area of the minor sector $OAPB.$

Answer 1

Given the radius of the circle centered at $O$ is $30$ cm.

Also $\angle AOB={120}^o$.

Then the area of the minor sector $APB$ is

$\frac{120}{360}\times \pi \times {30}^2$

$=\frac{\pi }{3}\times {30}^2$

$=300\pi$ cm${}^2$.