Question

$AB$ and $CD$ are respectively arcs of two concentric circles of radii 21$cm$ and 7$cm$ with centre $O$ . If $\lfloor AOB={30}^{\circ }$ .the area of the shaded region.

Answer 1

Shaded area = Area of sector OAB - Area of sector OCD

Shaded region = $(\frac{30}{360}\times \frac{22}{7}\times 21\times 21-\frac{30}{360}\times \frac{22}{7}\times 7\times 7)$$c{m}^2$

Shaded region =$\frac{30}{360}\times \frac{22}{7}\times (21\times 21-7\times 7)$$c{m}^2$

Shaded area = $\frac{11}{42}\times (21+7)\times (21-7)$$c{m}^2$

Shaded region = $\frac{11}{42}\times 28\times 14$ $c{m}^2$ = $102.67$ $c{m}^2$