Question

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

• A. $\frac{208}{5}c{m}^2$
• B. $\frac{358}{6}c{m}^2$
• C. $\frac{308}{3}c{m}^2$
• D. $\frac{108}{3}c{m}^2$

Answer 1

The correct option is C

$\frac{308}{3}c{m}^2$

Radius of the larger circle, R = 21 cm
Radius of the smaller circle, r = 7 cm
Angle made by sectors of both concentric circles $={30}^{\circ }$
Area of the larger sector $=\left(\frac{{30}^{\circ }}{{360}^{\circ }}\right)\times \pi R^{2}c{m}^2$
$=\frac{1}{12}\times \frac{22}{7}\times {21}^{2}c{m}^2$
$=\frac{231}{2}c{m}^2$
Area of the smaller circle $=\left(\frac{{30}^{\circ }}{{360}^{\circ }}\right)\times \pi r^{2}c{m}^2$
$=\frac{1}{12}\times \frac{22}{7}\times 7^{2}c{m}^2$
$=\frac{77}{6}c{m}^2$
Area of the shaded region $=\frac{231}{2}-\frac{77}{6}c{m}^2$
$=\frac{616}{6}c{m}^2=\frac{308}{3}c{m}^2$