Answer
$\pi \ mm$
Work Step by Step
In order to get the arc length $l$, we need to multiply the circumference $C$ by $\dfrac{120^{\circ}}{360^{\circ}}$.
$C=2\pi r= (2 \pi)(3)=6 \pi \ mm$
Further, we have: $l=\dfrac{120^{\circ}}{360^{\circ}} \times 6 \pi=2 \pi \ mm$
Next, the length of the semi-circle can be found as: $l=\dfrac{6 \pi}{2}=3 \pi \ mm$
Thus, the length of the third arc is equal to $l=6 \pi-3 \pi-2\pi=\pi \ mm$
