Question

A portion of the circle with centre $O$ is shaded as in the figure above. If the area of the shaded region is $12\pi$, and the angle subtended by the minor sector is ${60}^{\circ }$, what is the area of the circle?

• A. $2\pi$
• B. $10\pi$
• C. $24\pi$
• D. $48\pi$
• E. $72\pi$

Answer 1

The correct option is E $72\pi$

Given area of the shaded region is $12\pi$
Angle subtended by the minor sector $\mathring{60}$
We know that a circle is of 360 degree and the minor sector is 60 degree so $\frac{\mathring{60}}{\mathring{360}}=\frac{1}{6}$ is shaded region.
so area of the circle will be,
area of $\frac{1}{6}$ is $12\pi$
area of whole circle will be $12\pi \times 6=72\pi$