Question

In the figure given below. radius of a greater circle is $r$ cm. Find the area of non-shaded portion:

• A. $\frac{\pi r^2}{4}$ 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

Required area $=$ Area of $2$ small semi-circles $+$ Area of big semi circle
$\Rightarrow$$\frac{\pi {\left(\frac{r}{2}\right)}^2}{2}$ $+$ $\frac{\pi {\left(\frac{r}{2}\right)}^2}{2}$ $+$ $\frac{\pi r^2}{2}$

$\Rightarrow$ $\pi {\left(\frac{r}{2}\right)}^2+\frac{\pi r^2}{2}$
$\Rightarrow$$\frac{\pi r^2}{4}+\frac{\pi r^2}{2}=\frac{3\pi r^2}{4}$sq. cm