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 $6059.45\ cm^2$.