A steel wire when bent in the form of a square encloses an area of $121\ cm^2$. If the same wire is bent in the form of a circle, find the area of the circle.

Given:

A steel wire when bent in the form of a square encloses an area of $121\ cm^2$. The same wire is bent in the form of a circle.

To do:

We have to find the area of the circle.

Solution:

The steel wire is bent in the form of a square.

This implies,

Perimeter of the square $=$ Circumference of the circle

Let $s$ be the side of the square.

Therefore,

$s^2=121$

$s^2=(11)^2$

$s=11\ cm$

Perimeter $4s=4(11)\ cm$

$=44\ cm$

We know that,

Circumference of a circle of radius $r=2 \pi r$

Area of a circle of radius $r=\pi r^2$

Therefore,

Circumference of the circle formed $=2 \times \frac{22}{7} \times r$

$44=\frac{44}{7} \times r \mathrm{~cm}$

$r=7 \mathrm{~cm}$.

Area of the circle $=\frac{22}{7} \times(7)^{2} \mathrm{cm}^{2}$

$=22 \times 7 \mathrm{~cm}^{2}$

$=154 \mathrm{~cm}^{2}$

The area of the circle is $154\ cm^2$.   

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Updated on: 10-Oct-2022

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