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 ?

Answer: Option B

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