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A wire when bent in the form of square, encloses an area of $146.41\ cm^2$. If this wire is straighten and then bent to form a circle, what will be the area of the circle so formed?
Given: A wire when bent in the form of square, encloses an area of $146.41\ cm^2$. If this wire is straighten and then bent to form a circle.
To do: To find the area of the circle.
Solution:
Area of square $=Side^2$
$Side^2=146.1\ cm^2$
$Side=12.1\ cm$
Perimeter$=4\times12.1=48.4$
Perimeter of circle$=2\times\pi\times r=48.4$
$\Rightarrow 2\times( \frac{22}{7})\times r=48.4$
$\Rightarrow r=\frac{48.4\times7}{44}$
$\Rightarrow r=7.7\ cm$
Area$=\pi r^2 =\frac{22}{7}\times( 7.7)^2 $
$=22\times7.7\times1.1$
$= 186.34\ cm^2$
Updated on: 10-Oct-2022
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