Question

$PQRS$ is a diameter of a circle whose radius is $r$. The length of $PQ,QR$ and $RS$ are equal. Semicircles are drawn on $PQ$ and $QS$ to create the shaded figure given. The perimeter of the shaded figure is

• A. $2\pi r$
• B. $\frac{4\pi r}{3}$
• C. $\frac{5\pi r}{3}$
• D. $\frac{3\pi r}{2}$

Answer 1

The correct option is A $2\pi r$

Diameter $PS=2R$

$\therefore$ $PQ=QR=RS=$ $\frac{2r}{3}$

$\therefore$ Perimeter of the shaded portion $=\frac{1}{2}(2\pi \times \frac{r}{3})+\frac{1}{2}(2\pi \times \frac{2r}{3})+\frac{1}{2}\left(2\pi r\right)$

$=\frac{\pi r}{3}+\frac{2\pi r}{3}+\pi r$

$=2\pi r$