Question 68·Medium·Geometry and Trigonometry

Use the formula $s = \dfrac{\theta}{360} \cdot 2\pi r$, where $s$ is arc length, $\theta$ is the central angle in degrees, and $r$ is the radius.

After plugging in $\theta = 120$ and $r = 6$, simplify the fraction $\dfrac{120}{360}$ first, then multiply the remaining numbers and $\pi$.

In Desmos, type the expression (120/360)*2*pi*6 to represent $\dfrac{120}{360} \cdot 2\pi \cdot 6$.

Look at the value Desmos gives for this expression and match it to the equivalent choice written in terms of $\pi$ among the answer options.

For a circle with radius $r$ and a central angle of $\theta$ degrees, the arc length $s$ is given by:

This formula takes the fraction of the full circle represented by the angle and multiplies it by the full circumference.

Here, the radius is $r = 6$ cm and the central angle is $\theta = 120^{\circ}$. Substitute these into the formula:

First simplify the fraction:

Now compute the product:

Combine $2$ and $6$:

Finally,

So the length of the arc is $4\pi$ centimeters, which corresponds to choice B.