Question

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

Answer 1

Step 1: Find the radius of the circle.

Given that, circumference of a circle is $22cm$.

Suppose, radius of the circle be $r$, then circumference of the circle is $2\mathrm{\pi r}$.

Therefore, $2\mathrm{\pi r}=22$

$\Rightarrow 2\times \frac{22}{7}\times r=22\left[\because \mathrm{\pi }\approx \frac{22}{7}\right]$

$\Rightarrow \frac{44}{7}\times r=22$

$\Rightarrow r=\frac{22\times 7}{44}$

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

Hence, radius of the circle is $\frac{7}{2}cm$.

Step 2: Find the area of the circle.

Formula for finding area of a circle with radius $r$ is ${\mathrm{\pi r}}^2$.

Radius $=\frac{7}{2}cm$

Area $=\mathrm{\pi }\times {\left(\frac{7}{2}\right)}^2$

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

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

Hence, area of the circle is $\frac{77}{2}{cm}^2$.

Step 3: Find area of a quadrant.

Area of a quadrant $=$Area $\times \frac{1}{4}$

$=\frac{77}{2}\times \frac{1}{4}$

$=9.625{cm}^2$

Hence, the area of a quadrant of the circle is $9.625{cm}^2$.