Question

A wire when bent in the form of a square enclose an area of 484 $c{m}^2$. If the same wire is bent in the form of a circle. Find the area of the circle.

Answer 1

Given that, a wire, when bent, is able to enclose a square having area $484c{m}^2$

We know that, area of square $=sid{e}^2$

$484=a^2$

$a=22cm$

We know that perimeter of the square $=4a$

$\begin{array}{c}=4\times 22\\ =88cm\end{array}$

Therefore the length of the wire $=88cm$

Now,

given that the same wire is bent into a form of circle

circumference of circle = length of the wire

$\begin{array}{c}2\pi r=88\\ 2\times \frac{22}{7}\times r=88\\ r=\frac{88\times 7}{22\times 2}\\ r=14cm\end{array}$

Area of circle

$\begin{array}{c}=\pi r^2\\ =\frac{22}{7}\times {\left(14\right)}^2\\ =\frac{22}{7}\times 14\times 14\\ =\frac{22}{7}\times 196\\ =616c{m}^2\end{array}$

Hence, the area of the circle is $616c{m}^2$.