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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 $154\ cm^2$.