Question

Find the area of the shaded portion in the figure if the diameter of the larger circle is 12 cm.

• A. 88.53 $c{m}^2$
• B. 69.43 $c{m}^2$
• C. 82.53 $c{m}^2$
• D. 70.71 $c{m}^2$

Answer 1

The correct option is D

70.71 $c{m}^2$

We need to find the area of the shaded part here. If we observe the figure, we can make out that the shaded region can be split into 2 semicircles, such that the diameter of the smaller semicircle is equal to the radius of the larger semicircle.

The radius of the larger semicircle R =$\frac{d}{2}$ = 6 cm

The area of the larger semicircle is =$\frac{1}{2}\times \pi \times R^2$ = $\frac{1}{2}\times \frac{22}{7}\times 6^2$ = 56.57 $c{m}^2$

The radius of the smaller semicircle r = $\frac{R}{2}$ = 3 cm

The area of the smaller semicircle = $\frac{1}{2}\times \pi \times 3^2$ = $\frac{1}{2}\times \frac{22}{7}\times 9$ = 14.14 $c{m}^2$

Therefore,The area of the shaded region = Area of the larger semicircle +Area of the smaller semicircle = 56.57 + 14.14 = 70.71 $c{m}^2$

The area of the shaded region is 70.71 $c{m}^2$