#### Answer

$r=8$ 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: $14\pi=(r)(\frac{7\pi}{4})$
Step 4: $14=(r)(\frac{7}{4})$
Step 5: Multiplying both sides by 4, $14\times4=r\times\frac{7}{4}\times4$
Step 6: $56=7r$
Step 7: Therefore, $r=8$ units