Question

A steel wire when bent in the form of a square encloses an area of $121sq.cm$, if the same wire is bent into the form of a circle, find the area of the circle.

Answer 1

Given that

$\Rightarrow$Area of square$=121$sq.cm

$\Rightarrow$Therefore, length of wire$=\sqrt{121}$cm

$\Rightarrow$ length of wire$=11$cm

This wire is bent in form of circle.

$\Rightarrow 2\pi r=11$

$\Rightarrow r=\frac{11}{2\pi }$

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

$\Rightarrow$Area of circle$=\pi (\frac{11}{2\pi }{)}^2$

On solving we get

$\Rightarrow$Area of circle$=\frac{121}{4}c{m}^2$