Question

The area of a square and a circle are equal. The radius of the circle is $r$ and the side of the square is $s$. Find the circumference of the circle in terms of $s$.

• A. $\left(2s\right)\sqrt{\pi }$
• B. $\left(3s\right)\sqrt{\pi }$
• C. $\left(4s\right)\sqrt{\pi }$
• D. $\left(s\right)\sqrt{\pi }$

Answer 1

The correct option is A $\left(2s\right)\sqrt{\pi }$

Area of circle $=\pi r^2$

Area of square $=S^2$

$\pi r^2=S^2$

$\Rightarrow r=\frac{S}{\sqrt{\pi }}$

Circumference = $2\pi r=2\pi \left(\frac{S}{\sqrt{\pi }}\right)$

$=\left(2S\right)\sqrt{\pi }$