Question

Find the area of the shaded region in Fig, if radii of the two concentric circles with centre O are 7 cm and 14 cm respectively and $\angle AOC={40}^{\circ }$.

• A. $50c{m}^2$
• B. $48c{m}^2$
• C. $51c{m}^2$
• D. $36c{m}^2$

Answer 1

The correct option is C

$51c{m}^2$

Radius of inner circle = 7 cm
Radius of outer circle = 14 cm
Angle made by sector = ${40}^{\circ }$
Area of the sector $OAC=\left(\frac{{40}^{\circ }}{{360}^{\circ }}\right)\times \pi r^{2}c{m}^2$
$=\frac{1}{9}\times \frac{22}{7}\times {14}^2=68.44c{m}^2$

Area of the sector $OBD$
$=\left(\frac{{40}^{\circ }}{{360}^{\circ }}\right)\times \pi r^{2}c{m}^2$$=\frac{1}{9}\times \frac{22}{7}\times 7^2=17.11c{m}^2$
Area of the shaded region ABDC
= Area of the sector OAC - Area of the sector circle OBD
$=68.44c{m}^2-17.11c{m}^2=51.33c{m}^2$