Question

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

Answer 1

Area of sector AOB

Radius $r=21cm$

And $\theta ={30}^o$

Area of sector AOB $=\frac{\theta }{360}\times \pi r^2$

$=\frac{30}{360}\times \frac{22}{7}\times 21\times 21$

$=\frac{231}{2}c{m}^2$

Area of sector COD

Radius $r=7cm$

And $\theta ={30}^o$

Area of sector COD $=\frac{\theta }{360}\times \pi r^2$

$=\frac{30}{360}\times \frac{22}{7}\times 7\times 7$

$=\frac{77}{6}c{m}^2$

Now,

Area of shaded region $=\frac{231}{2}-\frac{77}{6}$

$=\frac{3\times 231-77}{6}$

$=\frac{693-77}{6}$

$=\frac{616}{6}$

$=\frac{308}{3}$