Question

If the angle of the sector with radius 3 cm is ${120}^{\circ }$, then its area is:

• A. $2\pi {\text{cm}}^2$
• B. $3\pi {\text{cm}}^2$
• C. $\pi {\text{cm}}^2$
• D. $6\pi {\text{cm}}^2$

Answer 1

The correct option is B $3\pi {\text{cm}}^2$

When the angle of the sector is ${360}^{\circ }$, then the sector will be a whole circle, so its area $=\pi r^2$

When the angle is $1^{\circ }$, area of the sector $=\frac{\pi r^2}{{360}^{\circ }}$

So, when the angle is $\theta$, area of the sector $=\theta \times \frac{\pi r^2}{{360}^{\circ }}=\frac{\theta }{{360}^{\circ }}\times \pi r^2$

Given, $r=3\text{cm},\theta ={120}^{\circ }$
$\therefore \text{Area of the sector =}\frac{{120}^{\circ }}{{360}^{\circ }}\times \pi \times 3^2$

$=\frac{{120}^{\circ }}{{120}^{\circ }\times 3}\times \pi \times 9$

$=\frac{1}{3}\times \pi \times 9$

$=3\pi {\text{cm}}^2$