Question

A copper wire when bent in the form of a square encloses an area of $484c{m}^2$. If the same wire is bent into the form of a circle, find the area enclosed by it.

Answer 1

We have, Area of the square $=a^2=484c{m}^2$

$\therefore$ Side of the square $=\sqrt{484}cm=22cm$

So, Perimeter of the square $=4\left(side\right)=(4\times 22)cm=88cm$

Let $r$ be the radius of the circle. Then, according to equation,

Circumference of the circle = Perimeter of the square

$\Rightarrow 2\pi r=88\Rightarrow 2\times \frac{22}{7}\times r=88$

$\Rightarrow r=\frac{88\times 7}{2\times 22}\Rightarrow r=14cm$

$\therefore$ Area of the circle $=\pi r^2=\{\frac{22}{7}\times (14{)}^2\}c{m}^2=616c{m}^2$