Here is the question:
The surface $S$ shown here has boundary the circle of radius $2$ in the $xz$-plane. With respect to the normal vector field indicated, compute the flux of $G = \langle 0, 3, 0 \rangle$ through $S$.
Based on the divergence theorem, since $\nabla\cdot G = 0$, I assume that the flux would also be $0$. However, I'm not sure whether the divergence theorem applies for such surfaces that seem to have holes in them. I also don't know what it means when the question says "with respect to the normal vector field indicated." I see that the vector $n$ is labeled in the diagram, but I have no idea how to use that information. Any help or clarification on this problem would be appreciated.