Question

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

(a)
(b)
(c)
(d)

Answer 1

(a) $\sqrt{\mathrm{\pi }}:1$

Let the side of the square be x cm and the radius of the circle be r cm.
Area of the square = Area of the circle
⇒ (x)² = ${\mathrm{\pi r}}^2$
∴ Side of the square (x) = $\sqrt{\mathrm{\pi }}r$
Required ratio = $\frac{\mathrm{Side}\mathrm{of}\mathrm{the}\mathrm{square}}{\mathrm{Radius}\mathrm{of}\mathrm{the}\mathrm{circle}}$
= $\frac{x}{r}=\frac{\sqrt{\mathrm{\pi }}r}{r}=\frac{\sqrt{\mathrm{\pi }}}{1}=\sqrt{\mathrm{\pi }}:1$