An arc AB of a sector of a circle subtends an angle 110° at the centre of the circle. Find the angle subtended by the arc at the circumference.

Step 1: The formula for the length of an arc is
$l = r \theta$
where $l$ is the arc length, $r$ is the radius, and $\theta$ is the central angle in radians.

Step 2: Convert the central angle from degrees to radians:
$\theta = 60^\circ \times \frac{\pi}{180} = \frac{\pi}{3}$ radians.

Step 3: Substitute the known values into the formula ($l = 3\pi$ cm, $\theta = \frac{\pi}{3}$ rad):
$3\pi = r \times \frac{\pi}{3}.$

Step 4: Solve for the radius $r$:
$r = 3\pi \div \frac{\pi}{3} = 3\pi \times \frac{3}{\pi} = 9.$
The radius of circle B is $9$ cm.

$\boxed{9 \ cm}$