A piece of wire is bent to form a square of area $121\ cm$. The same piece of wire is bent to form a circle. Find area of the circle.[Take $\pi=\frac{22}{7}]$.


Given: A piece of wire is bent to form a square of area $121\ cm^2$. The same piece of wire is bent to form a circle.

To do: To find area of the circle.

Solution:


As given, Area of the square$=121\ cm^2$


Let $a$ be the side of the square.

Area of the square $=a^2$

$\Rightarrow a^2=121$

$\Rightarrow a=\sqrt{121}$

$\Rightarrow a=11\ cm$

Therefore, the perimeter of the square$=4a$

$=4\times11$

$=44\ cm$

$\because$ Square is formed when the wire is bent. Therefore, length  of the wire is equal to perimeter of the square.

Length of the wire $l=44\ cm$

Now, the wire is bent to form a circle. Length of the wire would be equal to the circumference of the circle. Let $r$ be the radius of the circle.

$\therefore$ Perimeter$( circumference)$ of the circle $=2\pi r$

$\Rightarrow 2\pi r=44$

$\Rightarrow r=\frac{44}{2\pi}$

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

$\Rightarrow r=7\ cm$

$\therefore$ Area of the circle$=\pi r^2$

$=\frac{22}{7}\times7^2$

$=154\ cm^2$

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

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Updated on: 10-Oct-2022

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