In terms of pi, what is the length of an arc which subtends an angle of 30^ at the centre of a circle of radius 3(1)/(2) cm?

The angle subtended at the centre is $\theta = 30^\circ$.
The radius of the circle is $r = 3\frac{1}{2}$ cm.
The formula for the length of an arc ($L$) is:

$$L = \frac{\theta}{360^\circ} \times 2\pi r$$

$$L = \frac{30^\circ}{360^\circ} \times 2\pi \left(\frac{7}{2}\right)$$

Simplify the fraction $\frac{30}{360}$:

$$\frac{30}{360} = \frac{1}{12}$$

Now substitute this back into the formula:

$$L = \frac{1}{12} \times 2\pi \times \frac{7}{2}$$ $$L = \frac{1}{12} \times 7\pi$$ $$L = \frac{7\pi}{12} \text{ cm}$$

The length of the arc in terms of $\pi$ is $\frac{7\pi}{12}$ cm.

The final answer is $\frac{7\pi}{12} \text{ cm}$.