Question

In the figure given above, radius of a greater circle is $rcm$. Find the area of non-shaded portion

• A. $\frac{9\pi r^2}{16}sq.cm$
• B. $\frac{3\pi r^2}{4}sq.cm$
• C. $2\pi r^{2}sq.cm$
• D. $\frac{4\pi r^2}{3}sq.cm$

Answer 1

The correct option is B $\frac{3\pi r^2}{4}sq.cm$

Radius of big semicircle $=r$

Area of big semicircle $=\frac{\pi r^2}{2}$

Radius of small semicircles $=r/2$

Area of smaller semicircle $=\frac{1}{2}\times \frac{\pi r^2}{4}$

Area of 2 smaller semicircles $=\frac{\pi r^2}{4}$

Area of non-shaded region $=$Area of big semicircle $+2\times$ Area of the smaller semicircles

Area of non-shaded region $=\frac{\pi r^2}{2}+\frac{\pi r^2}{4}=\frac{3\pi r^2}{4}$