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The circumference of a circle is $22\ cm$. Calculate the area of its quadrant $( in\ cm^{2})$.
Given: The circumference of a circle is $22\ cm$.
To do: To calculate the area of its quadrant $( in\ cm^{2})$.
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 $=\frac{\pi r^{2}}{4}$
$=\frac{22}{7}\times ( \frac{7}{2})^{2}\times\frac{1}{4}$
$=\frac{77}{8}\ cm^{2}$.
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