To determine the length of the arc, we first solve the circumference of the circle using the formula C = 2πr.
Based on the circle, its radius is 6 cm.
[tex]C=2\times\pi\times6cm[/tex][tex]C=12\pi\text{ }cm[/tex]
Therefore, its circumference is 12π cm.
Next, we multiply the circumference by the ratio of its intercepted central angle and the 1 whole revolution.
In this case, the ratio is 120°/360°
[tex]ArcLength=\frac{120}{360}\times12\pi\text{ }cm[/tex][tex]ArcLength=\frac{1}{3}\times12\pi\text{ }cm[/tex][tex]ArcLength=4\pi\text{ }cm[/tex]
Therefore, the length of arc MN is 4π cm. (Option 4)
