Question

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

Answer 1

Step 1: Find the radius of the circle.

Given that the circumference is $22cm$.

Suppose, the radius of the circle is $r$.

Then the circumference of the circle is $2\mathrm{\pi r}$.

By the problem, $\begin{array}{rcl}2\mathrm{\pi r}& =& 22\end{array}$

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

$\Rightarrow$ $\begin{array}{rcl}\frac{44}{7}\times \mathrm{r}& =& 22\\ & & \end{array}$

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

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

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

Step 2: Find the area of the circle.

The formula for finding the area of a circle with radius $r$ is , Area $={\mathrm{\pi r}}^2$.

Here, $r=\frac{7}{2}$

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

$$\begin{gathered} =\frac{22}{7}\times \frac{7}{2}\times \frac{7}{2}\left[\because \mathrm{\pi }\approx \frac{22}{7}\right] \\ =\frac{11\times 7}{2} \\ =\frac{77}{2} \\ =38.5{cm}^2 \end{gathered}$$

Hence, the area of the circle is $38.5{cm}^2$.