Question 668·Medium·Math

No Desmos needed. The angle gives a simple fraction, and the remaining products each take one multiplication. A central angle has its corner at the circle’s center. Compare the given angle with a full $360^\circ$ turn. Divide: $\frac{120}{360}=\frac13$. The angle’s fraction of a full turn is the arc’s fraction of the circumference. So the arc covers one-third of the circle.

The circumference is the distance around the whole circle, given by $C=2\pi r$. The radius is $6$ centimeters. Substitute it: $C=2\pi(6)$. Multiply $2$ by $6$: $C=12\pi\text{ cm}$.

The arc is one-third of the circumference, not one-third of the radius. Write its length $L$ as that part of the whole: $L=\frac13(12\pi)$. Multiply: $L=4\pi\text{ cm}$. The arc is $4\pi$ centimeters long. Choice B.