Answer
$r=6$ units
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, r is the radius and $\theta$ is the central angle of measure in radians.
Step 2: $s=r\theta$
Step 3: $3\pi=(r)(\frac{\pi}{2})$
Step 4: $3=(r)(\frac{1}{2})$
Step 5: Multiplying both sides by 2, $3\times2=r\times\frac{1}{2}\times2$
Step 6: $6=r$
Step 7: Therefore, $r=6$ units
