The area of a sector of a circle of radius 6 cm with central angle 120° is:

The correct option is 12π cm².

To find the area of a sector of a circle, we use the formula for the area of a sector:

$\text{Area of sector}=\frac{\theta }{360°}\times \pi r^2$

From the given problem, we have the following values:
Radius ($r$) = 6 cm
Central angle ($\theta$) = 120°

Now, let's substitute these values into the formula:

$\text{Area of sector}=\frac{120°}{360°}\times \pi \times 6^2$

Simplify the fraction:

$\frac{120°}{360°}=\frac{1}{3}$

Calculate the square of the radius:

$6^2=36$

Now, substitute these back into the expression:

$\text{Area of sector}=\frac{1}{3}\times \pi \times 36$

$\text{Area of sector}=12\pi {\text{cm}}^2$

Thus, the area of the sector is 12π cm².