Question

In Figure, two concentric circles with centre O, have radii $21cm$ and $42cm$. If $\angle AOB={60}^{\circ }$, find the area of the shaded region. [Use $\pi =\frac{22}{7}$]

Answer 1

Given:

Radii of inner circle $=21cm=r$

Radii of outer circle $=42cm=R$

$\angle AOB=\theta ={60}^o$

Area of ring $=\pi (R^2-r^2)$

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

The area of shaded region $=$ Area of ring $–$ Area of $ABDC$

$=$ Area of ring $–$ [Area of sector of outer circle $–$ Area of sector of inner circle]

$=\pi (R^2-r^2)-\frac{\pi (R^2-r^2)}{1}\times \frac{\theta }{360}$

$=\pi [R^2-r^2](1-\frac{\theta }{360})$

$=\frac{22}{7}[{42}^2-{21}^2](1-\frac{60}{360})$

$=3465$ $c{m}^2$