To find the length of the arc formed by a central angle in a circle, you can use the formula:
\[ \text{Arc Length} = r \cdot \theta \]
where \( r \) is the radius and \( \theta \) is the central angle in radians.
Given:
- Radius \( r = 27 \) mm
- Central angle \( \theta = \frac{2\pi}{3} \) radians
Now, substitute the values into the formula:
\[ \text{Arc Length} = 27 \cdot \frac{2\pi}{3} \]
Calculating this step-by-step:
\[ \text{Arc Length} = 27 \cdot \frac{2\pi}{3} = \frac{54\pi}{3} = 18\pi \]
So, the length of the arc is \( 18\pi \) mm.
Thus, the correct response is:
18π mm