Question

Find the area of a circle whose circumference is $22\text{cm}$.

Answer 1

Step 1 : Calculation of radius of the circle.

It is given that circumference is $22\text{cm}$.

The circumference of a circle is calculated by the formula,

$\mathbf{\text{C}}\mathbf{=}\mathbf{2}\mathit{\pi }\mathit{r}$, where $\text{C}$ is the circumference and $r$ is the radius of a circle.

$$\begin{gathered} \therefore 2\pi r=22 \\ \Rightarrow 2\left(\frac{22}{7}\right)r=22\left[\because \pi =\frac{22}{7}\right] \\ \Rightarrow 2r=22\times \frac{7}{22} \\ \Rightarrow r=\frac{7}{2} \\ \Rightarrow r=3.5\text{cm} \end{gathered}$$

Step 2 : Calculation of the area of the circle.

The area of the circle is given by,

$\mathit{A}\mathbf{=}\mathit{\pi }{\mathit{r}}^{\mathbf{2}}$, where $A$ is the area and $r$ is the radius of a circle.

$\begin{array}{rcl}\therefore A& =& \pi r^2\\ & =& \frac{22}{7}{\left(3.5\right)}^2\left[\because \pi =\frac{22}{7}\right]\\ & =& \frac{22}{7}(3.5)(3.5)\\ & =& 22(0.5)(3.5)\\ & =& 11\times 3.5\\ & =& 38.5{\text{cm}}^2\end{array}$

Final Answer

Hence, the area of the circle with the given circumference is $\mathbf{38}\mathbf{.}\mathbf{5}\mathbf{}{\mathbf{\text{cm}}}^{\mathbf{2}}$.