If the perimeter of a square is equal to the radius of a circle whose area is 39424 sq. m. What is the area of the square ?

A. 441 sq.m

B. 784 sq.m

C. 1225 sq.m

D. Cannot be determined

E. None of these

Answer: Option B

Solution(By Examveda Team)

Let the radius of the circle be R cm
Then,
$$\eqalign{ & \pi {R^2} = 39424 \cr & \Rightarrow {R^2} = 39424 \times \frac{7}{{22}} = 12544 \cr & \Rightarrow R = 112\,cm \cr} $$
Perimeter of the square = 112 cm
Side of the square :
$$\eqalign{ & = \left( {\frac{{112}}{4}} \right)cm \cr & = 28\,cm \cr} $$
∴ Area of the square :
$$\eqalign{ & = \left( {28 \times 28} \right)c{m^2} \cr & = 784\,c{m^2} \cr} $$