Question

The area of a circle and a square are equal, the ratio of the sides of the square to the radius of the circle is

• A. $2:\sqrt{\pi }$
• B. $\sqrt{\pi }:1$
• C. $\sqrt{2}:1$
• D. $1:\sqrt{2}$
• E. $Noneofthese$

Answer 1

The correct option is

B

$\sqrt{\pi }:1$

Area of square$=a^2$

Area of circle$=\pi r^2$

According to question,

$a^2=\pi r^2$

$\frac{a^2}{r^2}=\pi$

$\frac{a}{r}=\frac{\sqrt{\pi }}{1}$

$a:r=\sqrt{\pi }:1$

Option$\left(B\right)$ is correct.