Question

In fig. 9.32 three semicircles of diameter AB = 8cm. BC = 4 cm and CD = 2 cm are drawn.
Find i) Area of shaded portion.

Answer 1

Let the diameter of the 1st semicircle be AB i.e. 8 cm.
Then its radius (r₁) = $\frac{8}{2}=4\mathrm{cm}$
Let the diameter of the 2nd semicircle be BC i.e. 4 cm.
Then its radius (r₂) = $\frac{4}{2}=2\mathrm{cm}$
Let the diameter of the 3rd semicircle be CD i.e. 2 cm.
Then its radius (r₃) = $\frac{2}{2}=1\mathrm{cm}$

∴ Area of the shaded portion = area of 1st semicircle + area of 2nd semicircle + area of 3rd semicircle
$$\begin{gathered} =\frac{\pi {r_1}^2}{2}+\frac{\pi {r^2}_2}{2}+\frac{\pi {r^2}_3}{2} \\ =\frac{\pi }{2}\left({r_1}^2+{r^2}_2+{r^2}_3\right) \\ =\frac{22}{2\times 7}\left(4^2+2^2+1^2\right) \\ =\frac{11\times 21}{7}{\mathrm{cm}}^2 \\ =33{\mathrm{cm}}^2 \end{gathered}$$