Question

a sector of a circle has a radius of 12 in. and a central angle that measures $120^\circ$.
what is the exact area of the sector?
$\bigcirc$ $151\pi \text{ in}^2$
$\bigcirc$ $150.72 \text{ in}^2$
$\bigcirc$ $48\pi \text{ in}^2$
$\bigcirc$ $150.8 \text{ in}^2$

Explanation:

Step1: Recall sector area formula

The formula for the area of a sector is $A = \frac{\theta}{360^\circ} \times \pi r^2$, where $\theta$ is the central angle and $r$ is the radius.

Step2: Substitute given values

Substitute $\theta = 120^\circ$, $r = 12$ in:
$A = \frac{120^\circ}{360^\circ} \times \pi \times (12)^2$

Step3: Simplify the expression

First simplify $\frac{120^\circ}{360^\circ} = \frac{1}{3}$, and $(12)^2 = 144$:
$A = \frac{1}{3} \times \pi \times 144 = 48\pi$

Answer:

48π in² (Option: 48π in²)