Question

Find the area of the shaded region (in $c{m}^2$) as shown in figure of the two concentric circles with centre O and radius 7 $cm$ and 14 $cm$ respectively. Given $\angle$AOC = ${40}^{\circ }$.
(use $\pi$ = $\frac{22}{7}$)

• A. 42.1 $c{m}^2$
• B. 51.32 $c{m}^2$
• C. 67.8 $c{m}^2$
• D. 96.5 $c{m}^2$

Answer 1

The correct option is B

51.32 $c{m}^2$

Given: radius for sector OAC = 14 $cm$ and angle subtended = ${40}^{\circ }$ and
radius for sector OBD = 7 $cm$ and angle subtended = ${40}^{\circ }$

Area of Sector = $\frac{x^{\circ }}{{360}^{\circ }}\times \pi r^2$
Required area = [Area of sector OAC – Area of sector OBD]
=$\frac{40}{360}\times \frac{22}{7}\times {14}^2–\frac{40}{360}\times \frac{22}{7}\times 7^2$
= 68.42 - 17.1
= $51.32c{m}^2$
$\therefore$ Area of shaded region = $51.32c{m}^2$