Question

A steel wire, when bent in the form of a square, encloses an area of 121 sq. cm. The same wire is bent in the form of a circle. Find the area of the circle.

Answer 1

Side of the square = $\sqrt{area}=\sqrt{121}=11cm$

Perimeter of the square = $4\times side=44cm$

Therefore, length of the wire = 44 cm

We know,

Circumference of the circle = Length of the wire

Therefore, Circumference of the circle = 44 cm

Let the radius of the circle be r cm.

Then, $2\pi r=44$

$2\times \frac{22}{7}\times r=44$

$r=7cm$

Therefore, area of the circle = $\pi r^2=\frac{22}{7}\times 49=154c{m}^2$.