Question

what is the area of the shaded sector of the circle?$\bigcirc$ $9pi$ units$^{2}LXB0\bigcirc$ $81pi$ units$^{2}$$\bigcirc$ $162pi$ units$^{2}$the circle has center l, radius 9, and the central angle of the shaded sector klm is $120^{circ}$

Explanation:

Step1: Find full circle area

The formula for the area of a circle is $A = \pi r^2$. Here, $r=9$, so:
$A = \pi (9)^2 = 81\pi$

Step2: Calculate sector fraction

The sector angle is $120^\circ$, so the fraction of the circle is $\frac{120}{360} = \frac{1}{3}$.

Step3: Compute sector area

Multiply the full area by the fraction:
$\text{Sector Area} = 81\pi \times \frac{1}{3}$

Answer:

$27\pi$ units$^2$ (Option B. $27\pi$ units$^2$)