Question

In the given figure, the area of shaded region is

• A. $462c{m}^2$
• B. $308c{m}^2$
• C. $616c{m}^2$
• D. $154c{m}^2$

Answer 1

The correct option is D $154c{m}^2$

Area of the shaded region = Area of circle with center at $O$ - Area of semicircle with center at $O$-Area of smaller semicircle with radius $r^{{}^{\prime }}$-Area of smaller semicircle with radius $r^{{}^{\prime }}$
Here, $r=\frac{28}{2}=14$
$r^{{}^{\prime }}=\frac{r}{2}$
$=>r^{{}^{\prime }}=\frac{14}{2}$
$=>r^{{}^{\prime }}=7$
Area of the shaded region $=\pi r^2-\frac{\pi r^2}{2}-\frac{\pi r^{{}^{\prime }2}}{2}-\frac{\pi r^{{}^{\prime }2}}{2}$
$=\frac{\pi r^2}{2}-\pi r^{{}^{\prime }2}$
$=\frac{\pi \times {14}^2}{2}-\pi 7^2$
$=\frac{22\times 14\times 14}{2\times 7}-\frac{22\times 7\times 7}{7}$
$=22\times 14-22\times 7$
$=22\times 7$
$=154c{m}^2$