Question

In the given figure, two concentric circles with center O have radii 21 cm and 42 cm. If $\angle AOB={60}^0$, then find the area of the shaded region.

Answer 1

The radius of larger circle $42cm$

The radius of smaller circle $21cm$

The area of ring is

$\pi (R^2-r^2)$

$\frac{22}{7}\times (1764-441)$

$\frac{22}{7}\times 1323=4158c{m}^2$

The area of ${60}^{\circ }$ portion is

$\frac{60}{360}\times 4158=\frac{4158}{6}=693c{m}^2$

The area of shaded region is $4158-693=3465c{m}^2$