Question

In the given figure the boundary of the shaded region consists of your semicircular are two smallest being equal If diameters of the largest in $14$ cm and that of the smallest in $3.5$ cm Calculate the shaded area.

Answer 1

Given $\Rightarrow$ Diameter of largest semi circle$\left(2R\right)=14cm$

Diameter of small semicircle $\left(2r_1\right)=3.5cm$

Diameter of two other semi circle$=2\times 3.5=7cm$

Therefore, diameter of third small semi circle$\left(2r_2\right)=14-7=7cm$

Area of shaded region=Area of largest semi circle$-2\times$area of small semi circle+area of semicircle of radius$\left(r_2\right)=7cm$

Area of shaded region$=\frac{\pi R^2}{2}+\frac{\pi r_2^2}{2}-2\times \frac{\pi r_1^2}{2}$

Area of shaded region$=\frac{1}{2}\times \frac{22}{7}\times 7\times 7+\frac{1}{2}\times \frac{22}{7}\times \frac{7}{2}\times \frac{7}{2}-2\times \frac{1}{2}\times \frac{22}{7}\times \frac{3.5}{2}\times \frac{3.5}{2}$

$=77+19.25-9.625=86.625c{m}^2$