The circumference of a circle is equal to the side of a square whose area measures 407044 sq.cm. What is the area of the circle ?

A. 22583.2 sq.cm

B. 32378.5 sq.cm

C. 39483.4 sq.cm

D. 41263.5 sq.cm

E. Cannot be determined

Answer: Option B

Solution(By Examveda Team)

Area of the square = 407044 cm²
Side of the square = $$\sqrt {407044} $$  cm = 638 cm
Circumference of circle = 638 cm
Let the radius of the circle be R cm
Then,
$$\eqalign{ & 2\pi R = 638 \cr & \Rightarrow R = \frac{{638 \times 7}}{{2 \times 22}} \cr & \Rightarrow R = 101.5\,cm \cr} $$
∴ Area of the circle :
$$\eqalign{ & = \left( {\frac{{22}}{7} \times 101.5 \times 101.5} \right)c{m^2} \cr & = 32378.5\,\,c{m^2} \cr} $$