Question

The circumference of a circle is $8\text{cm}$. Find the approximate area of the sector whose central angle is ${72}^{\circ }$.

• A. $1.02{\text{cm}}^2$
• B. $3.12{\text{cm}}^2$
• C. $2.54{\text{cm}}^2$
• D. $4.2{\text{cm}}^2$

Answer 1

The correct option is A $1.02{\text{cm}}^2$

Given that, circumference of a circle is $8\text{cm}$ and the central angle of a sector is ${72}^{\circ }$
Now, circumference of a circle $=2\pi r$
$\Rightarrow 8=2\pi r$
$r=\frac{8\times 7}{22\times 2}$
$\pi =\frac{22}{7}$
$=\frac{14}{11}\text{cm}$
We know that, area of sector $=\frac{\theta }{360}\times \left(\pi r^2\right)$
$=\frac{72}{360}\times \frac{22}{7}\times \frac{14}{11}\times \frac{14}{11}$
$=1.02{\text{cm}}^2$
Hence, the required area of the sector is $1.02{\text{cm}}^2$