Question

A copper wire when bent in the form of a square encloses an area of $484c{m}^2$. The same wire is now bent in the form of a circle. Find the area enclosed by the circle.

Answer 1

We know that,

Area of a square $=(\text{side}{)}^2$

According to the question,

$\Rightarrow (\text{side}{)}^2=484$

$\begin{array}{cc}2& 484\\ 2& 242\\ 11& 121\\ 11& 11\\ & 1\end{array}$

$\Rightarrow (\text{side}{)}^2=484=2^2\times {11}^2$

$\Rightarrow \text{side}=22cm$

Therefore, total length of the wire $=4\times \text{side}=4\times 22=88cm$

Since, this wire in know bent into the shape of a circle.
Therefore, circumference of the circle with radius $r=2\pi r=88cm$

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

$\Rightarrow r=88\times \frac{7}{44}=14cm$

Hence, area of the circle so formed $=\pi r^2$

$=\frac{22}{7}\times 14\times 14$

$=616c{m}^2$

Hence, area now enclosed by the wire is $616c{m}^2$.