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Find the area of circle whose circumference is $276\ cm$.
Given:
Circumference of a circle is $276\ cm$.
To do:
We have to find the area of the circle.
Solution:
Let the radius of the circle be $r$.
We know that,
Circumference of a circle of radius $r=2 \pi r$
Area of a circle of radius $r=\pi r^2$
Therefore,
Circumference of the given circle $=2 \times \frac{22}{7} \times r$
$r=276\times\frac{7}{44} \mathrm{~cm}$
$r=\frac{69\times7}{11} cm$
$r=\frac{483}{11}\ cm$
Area of the given circle $=\frac{22}{7} \times(\frac{483}{11})^{2} \mathrm{cm}^{2}$
$=\frac{22}{7} \times \frac{483}{11} \times \frac{483}{11} \mathrm{~cm}^{2}$
$=\frac{2\times483\times69}{11} \mathrm{~cm}^{2}$
$=\frac{66654}{11} \mathrm{~cm}^{2}$
$=6059.45 \mathrm{~cm}^{2}$
The area of the circle is $6059.45\ cm^2$.
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