Can I use the divergence theorem to calculate the following:

$\displaystyle \vec{G} = -x^3\vec{i} - y^3\vec{j} - z^3\vec{k} $

Find the flux of the vector field out of the closed surface S. S is the boundary of the solid region W. W is the upper hemisphere of radius 3 centered at the origin.

well the divG I got is $\displaystyle -3x^2 -3y^2 -3z^2$, which is $\displaystyle -3(x^2 + y^2 + z^2) $ and this translates to $\displaystyle -3r^2 $ am I right? do I just then multiply this by the volume, which is $\displaystyle 18\pi $ in this case?