To find the length of the arc formed by a central angle in a circle, you can use the formula:
\[ \text{Arc Length} = r \theta \]
where:
- \( r \) is the radius of the circle,
- \( \theta \) is the central angle in radians.
In this case, the radius \( r \) is 27 millimeters, and the central angle \( \theta \) is \( \frac{2\pi}{3} \) radians.
Now, plug in the values:
\[ \text{Arc Length} = 27 \cdot \frac{2\pi}{3} \]
Now perform the multiplication:
\[ \text{Arc Length} = \frac{27 \cdot 2\pi}{3} = \frac{54\pi}{3} = 18\pi , \text{mm} \]
So, the length of the arc formed by that angle is:
\[ \boxed{18\pi , \text{mm}} \]
Thus, the correct response is 18π mm.