Lets assume that one side of square can be referred by 's'.

In the figure, it can be seen that a side of the square is equal to the diameter of the smaller circle.
Diameter of small circle = s
Radius of small circle = s / 2

The diagonal of the square is equal to the diameter of big circle
Diameter of big circle = s * (2)^0.5
Radius of big circle = (s * 2^0.5)/2

Area of small circle = pi * radius^2 = pi * (s/2)^2
Area of small circle = pi * (s^2)/4

Area of big circle = pi * radius^2 = pi * [(s * 2^0.5)/2]^2 = pi * [((s^2) * 2)/4]
Area of big circle = pi * [(s^2)/2]

Ratio of Area of big circle to Area of small circle = [pi * (s^2)/2] / [pi * (s^2)/4]
After cancelling out pi and s^2, we get:
Ratio of Area of big circle to Area of small circle = 4 / 2 = 2

Therefore, the answer is D) 2.