Question

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

Answer 1

Let a cm be the side of square. Then area of square is

$a^2=121$

$\Rightarrow a=11cm$

Now, length of the wire = Perimeter of the square = 4a = 44 cm

Let the radius of the circle be r. Then,

Circumference of circle = Length of wire

$\Rightarrow 2\pi r=44$

$\Rightarrow 2\times \frac{22}{7}\times r=44$

$\Rightarrow r=7cm$

Now, we will calculate area of the circle as $\pi r^2=\frac{22}{7}\times 7^2=154c{m}^2$