# Find the area of a quadrant of a circle whose circumference is 22 cm.

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Given:

The circumference of a circle is $22\ cm$.

To do:

We have to calculate the area of the quadrant.

Solution:

Let the radius of the circle is $=r\ cm$

Circumference of the circle $=22\ cm$

$\Rightarrow 2\pi r=22$

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

$\Rightarrow \frac{2}{7}\times r=1$

$\Rightarrow 2r=7$

$\Rightarrow r=\frac{7}{2}$

Area of the quadrant $=\frac{\pi r^{2}}{4}$

$=\frac{22}{7}\times ( \frac{7}{2})^{2}\times\frac{1}{4}$

$=\frac{77}{8}\ cm^{2}$.

Therefore, the area of the quadrant is $\frac{77}{8}\ cm^{2}$.

Updated on 10-Oct-2022 13:23:53