Question

The circumference of a circle is 88 cm. Find the area of the sector whose central angle is 72°.

Answer 1

Given:
Circumference of the circle = 88 cm
$\theta ={72}^{\circ }$
Area of the sector = ?

$$\begin{gathered} \mathrm{We}\mathrm{know}: \\ \mathrm{c}=2\mathrm{\pi r} \\ \Rightarrow 88=2\times \frac{22}{7}\times \mathrm{r} \\ \Rightarrow \mathrm{r}=\frac{88\times 7}{44} \\ \Rightarrow \mathrm{r}=14\mathrm{cm} \end{gathered}$$

Area of the sector = $\frac{\mathrm{\pi }{r}^2\mathrm{\theta }}{360}$

$$\begin{gathered} =\frac{22}{7}\times 14\times 14\times \frac{72}{360} \\ =123.2{\mathrm{cm}}^2 \end{gathered}$$