To find the length of an arc of a circle, you can use the formula:
\[ L = r \theta \]
where:
- \( L \) is the length of the arc,
- \( r \) is the radius of the circle, and
- \( \theta \) is the central angle in radians.
First, we need to convert the central angle from degrees to radians. The conversion from degrees to radians is given by:
\[ \theta \text{ (in radians)} = \theta \text{ (in degrees)} \times \frac{\pi}{180} \]
So for a central angle of 300 degrees:
\[ \theta = 300 \times \frac{\pi}{180} = \frac{300\pi}{180} = \frac{5\pi}{3} \text{ radians} \]
Now we can substitute \( r = 18 \) inches and \( \theta = \frac{5\pi}{3} \) radians into the arc length formula:
\[ L = 18 \times \frac{5\pi}{3} \]
Calculating this gives:
\[ L = \frac{18 \times 5\pi}{3} \]
Simplifying further:
\[ L = \frac{90\pi}{3} = 30\pi \]
Thus, the length of the arc is
\[ \boxed{30\pi} \text{ inches.} \]