Question

The area of a square is equal to the area of a circle. The ratio between the side of the square
and the radius of the circle is

(a) $\sqrt{\pi }$ : 1 (b) 1 : $\sqrt{\pi }$ (c) 1 : $\pi$ (d) $\pi$ : 1

Answer 1

Let a and r be respectively the side of the square and radius of the circle.
Here, the area of square is equal to the area of the circle. So
$$\begin{gathered} a^2=\pi r^2 \\ \Rightarrow \frac{{\mathit{a}}^{\mathit{2}}}{{\mathit{r}}^{\mathit{2}}}\mathit{=}\pi \\ \Rightarrow \frac{a}{r}=\sqrt{\pi } \end{gathered}$$
Hence, the correct option is (a).