Question

In the given figure, two concentric circles centred at O have a radius of $21cm$ and $42cm$. If $\angle AOB=60°$, find the area of the shaded region. (Use 𝝅=𝟐𝟐/𝟕).

Answer 1

The angle subtended by the major sector in the bigger circle is $300°(=360°-60°)$

Area of the major ​sector in the bigger circle $=\frac{\theta }{360°}\times \pi \times r^2$
$=\frac{300°}{360°}\times \frac{22}{7}\times {42}^{2}c{m}^2$ $=4620c{m}^2$
The radius of the smaller circle is $21cm.$
The angle subtended by the major sector in the smaller circle is $300°(=360°-60°)$
Area of the major ​sector in the smaller circle
$=\frac{\theta }{360°}\times \pi \times r^2$
$=\frac{300°}{360°}\times \frac{22}{7}\times {21}^{2}c{m}^2=1155c{m}^2$.
Area of the shaded region = Area of the major ​sector in the bigger circle − Area of the major ​sector in the smaller circle
Area of the shaded region
$=4620c{m}^2-1155c{m}^2=3465c{m}^2$