Question

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

Answer 1

REF.Image

Area of shaded region

= Area of sector AOB - Area of sector COD

Area of sector AOB.

radius =r= 21 cm; $\theta ={30}^{\circ }$

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

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

$=\frac{1}{12}\times 22\times 3\times 21$

$=\frac{231}{2}c{m}^2$ (OR) $115.5c{m}^2$

Area of sector COD :

radius = r = 7 cm ; $\theta ={30}^{\circ }$

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

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

$=\frac{1}{12}\times \frac{22}{7}\times 7\times 7$

$=\frac{77}{6}c{m}^2$ (OR) $12.83c{m}^2$

Area of shaded region = Area of sector OAB - Area of sector OCD

$=\frac{231}{2}-\frac{77}{6}$

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

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

Hence area of shaded region = $\frac{616}{6}=\frac{308}{3}c{m}^2$ (OR) $102.667c{m}^2$