Question

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

Answer 1

Radius of bigger circle = $42$ cm
Area of major sector in bigger circle = $\frac{\theta }{360}\pi r^2$ ($\theta$ being the angle subtended by major arc)

Area of major sector in bigger circle = $\frac{300}{360}\pi (42{)}^2$

Area of major sector in bigger circle = $4620c{m}^2$
Radius of smaller circle = $21$cm
Area of major sector = $\frac{\theta }{360}\pi r^2$ ($\theta$ being the angle subtended by major arc)

Area of major sector = $\frac{300}{360}\pi (21{)}^2$
Area of major sector = $1155c{m}^2$

Area of shaded portion = $4620-1155$ = $3465c{m}^2$