Ok, thanks. That makes sense now; so now I should say, for a volume containing a spherical shell of radius R centered at the origin:
\int_V \rho\cdot\delta (r-R)\cdot r^2\,dr\,sin\,\theta\, d\theta\, d\varphi=Q
\rho\int_0^\infty r^2 \delta (r-R)\, dr \int_0^\pi sin\,\theta\, d\theta...