A steel wire when bent in the form of a square encloses an area of $121 \mathrm{~cm}^{2}$. If the same wire is bent in the form of a circle, find the area of the circle.
Let a cm be the side of square. Then area of square is
$a^{2}=121 \mathrm{~cm}^{2}$
$a=\sqrt{121 \mathrm{~cm}^{2}}$
$a=11 \mathrm{~cm}$
We have,
length of wire $=$ perimeter of square
$=4 a \mathrm{~cm}$
$=4 \times 11 \mathrm{~cm}$
$=44 \mathrm{~cm}$
Let the radius of circle be r cm. Then,
circumference of circle $=$ length of wire
$2 \pi r=44 \mathrm{~cm}$
$2 \times \frac{22}{7} \times r=44 \mathrm{~cm}$
$r=7 \mathrm{~cm}$
Now, we will calculate area of circle.
Area of circle $=\pi r^{2} \mathrm{~cm}^{2}$
$=\frac{22}{7} \times 7 \times 7 \mathrm{~cm}^{2}$
$=154 \mathrm{~cm}^{2}$
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