If the length of a side of a square is same as length of the diameter of a circle, then the ratio of their areas is :

1. 1 : π

2. 2 : π

3. 4 : π

4. 8 : π

Given,

Diameter of circle = side of square = s

Area of square = s²

Radius = $\dfrac{\text{Diameter}}{2} = \dfrac{s}{2}$

Area of circle = πr²

= $\pi \Big(\dfrac{s}{2}\Big)^2$

= $\dfrac{πs^2}{4}$

Area of square : Area of circle

= s² : $\dfrac{πs^2}{4}$

= $\dfrac{s^2}{\dfrac{πs^2}{4}}$

= $\dfrac{4}{π}$

= 4 : π.

Hence, option 3 is the correct option.