A wire encloses an area of 616 $$cm^2$$ when it is bent in the form of a circle. If the wire is bent in the form of a square, then its area (in $$cm^2$$) is very nearly equal to: (Take $$\pi = \frac{22}{7}$$)

A wire encloses an area of 616 $$cm^2$$ when it is bent in the form of a circle.

area of circle = $$\pi\ \times\ \left(radius\right)^2$$

$$616=\frac{22}{7}\times\ \left(radius\right)^2$$

$$28=\frac{1}{7}\times\ \left(radius\right)^2$$

$$28\times\ 7=\ \left(radius\right)^2$$

$$(radius)^2 = 196$$

radius = 14 cm

If the wire is bent in the form of a square.

circumferences of circle = perimeter of square

$$2\times\ \pi\ \times\ radius\ =\ 4\times\ side$$

$$2\times\ \frac{22}{7}\ \times\ radius\ =\ 4\times\ side$$

$$\frac{11}{7}\ \times\ 14\ =\ \ side$$

$$11\ \times\ 2=\ \ side$$

side = 22 cm

Area of square = $$side\times\ side$$

= $$22\times22$$

= 484 $$cm^2$$