Question

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

Answer 1

Angle for shaded region = ${360}^{\circ }-{60}^{\circ }={300}^{\circ }$

Area of shaded region =$\frac{\pi \theta }{360}(R^2-r^2)$

= $\frac{22}{7}\times \frac{300}{360}[{42}^2-{21}^2]$

=$\frac{22}{7}\times \frac{5}{6}\times 63\times 21$

= 3465 cm${}^2$