Question

The circumference of a circle is 8 cm. Find the area of the sector whose central angle is 72°.

Answer 1

Let the radius of the circle be r.
​Now,
$$\begin{gathered} \mathrm{Circumference}=8 \\ \Rightarrow 2\mathrm{\pi }r=8 \\ \Rightarrow r=\frac{14}{11}\mathrm{cm} \end{gathered}$$
We have $r=\frac{14}{11}\mathrm{cm}\mathrm{and}\mathrm{\theta }=72°$
Area of sector = $\frac{\mathrm{\theta }}{{360}^{°}}\times \mathrm{\pi }{r}^2=\frac{72°}{360°}\times \frac{22}{7}\times {\left(\frac{14}{11}\right)}^2=1.02{\mathrm{cm}}^2$
Hence, the area of the sector of the circle is 1.02 cm².

Disclaimer : If we take the circumference of the circle is 8 cm then the area of the sector will be 1.02 cm². But if we take the circumference of the circle is 88 cm then the area of the sector will be 123.2 cm²