The area of a circle whose radius is the diagonal of a square whose area is 4 sq. units is :

Answer: Option D

Area of square = 4 sq.units
Side of square = $$\sqrt{4}$$ = 2 units
Diagonal of square = $$2\sqrt{2}$$ units
Radius of the circle = $$2\sqrt{2}$$ units
Radius of the circle :
$$\begin{array}{rl}& =\pi r^2\\ & =\pi \times {\left(2\sqrt{2}\right)}^2\\ & =8\pi \text{sq. units}\end{array}$$