Question

A steel wire when bent in the form of a square encloses an area of $121c{m}^2$. If the same wire is bent in the form of a circle. Find the area of the circle.(in $c{m}^2$)

Answer 1

Let 'a' be the side of the square.

Given, Area of the square $=121c{m}^2$

$\Rightarrow a^2=121$

$\Rightarrow a=\sqrt{121}cm$

$\Rightarrow a=11cm$

Primeter of the square $=4a$

$=4\left(11\right)cm$

$=44cm$

Since the same wire is bent in the form of a circle.

$\Rightarrow$ perimeter of the circle = perimeter of the square

$\Rightarrow 2\pi r=44$

$\Rightarrow r=44\times \frac{1}{2\pi }$

$=44\times \frac{1}{2\times \frac{22}{7}}$ $[using\pi =\frac{22}{7}]$

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

$=7cm$

Area of the circle $=\pi r^2$

$=\frac{22}{7}(7{)}^2$

$=22\times 7$

$=154c{m}^2$