The vector equation $\mathbf{r} \left( u, v \right) = u \cos v \mathbf{i} + u \sin v \mathbf{j} + v \mathbf{k}$, $0 \leq v \leq 3 \pi$, $0 \leq u \leq 1$, describes a helicoid (spiral ramp). What is the surface area?