Chapter 7 - Trigonometry and Periodic Functions - 7.3 Radians and Arc Length - Exercises and Problems for Section 7.3 - Exercises and Problems - Page 284: 38

$\frac{\pi}{9}$ rad.

Since $s=r\theta$ for an arc length $s$, dividing both sides by $r$ gives $$\theta=\frac{s}{r}$$ Using $s=2\pi \, \textrm{m.}$ and $r=18 \textrm{m.}$ yields $$\theta=\frac{2\pi \, \textrm{m.}}{18 \, \textrm{m.}}=\frac{\pi}{9} \, \textrm{rad.}$$