Answer
$27\pi$ radians
Work Step by Step
Step 1: The formula to be used here is $s=r\theta$ where $s$ is the length of the arc intercepted on a circle of radius $r$ by a central angle of measure $\theta$ radians.
Step 2: In this case, $r=3$ inches.
Step 3: Since the complete rotation of $60$ minutes is equal to $2\pi$ radians, $4.5$ hours therefore represent $4.5(2\pi)$ or $9\pi$ radians.
Step 4: The distance traveled by the tip of the minute hand is represented by the arc length $s$.
Step 5: Therefore $s=r\theta=(3)(9\pi)=27\pi$ radians