The basic building block for volume integrals is the infinitesimal volume, obtained by chopping up the volume into small “parallelepipeds”. Our approach for surface integrals can be extended to volume integrals using the triple product. The volume element becomes \begin{equation} \dV = (d\rr_1\times d\rr_2)\cdot d\rr_3 \end{equation} for the $d\rr$'s computed for (any!) 3 non-coplanar families of curves. 1) (The volume element is often written as $dV$, but we prefer $\dV$ to avoid confusion with the electrostatic potential $V$.) Using the natural families of curves in spherical coordinates, we could take \begin{eqnarray} d\rr_1 &=& r \,d\theta \,\that \\ d\rr_2 &=& r \,\sin\theta \,d\phi \,\phat \end{eqnarray} as before, and add \begin{equation} d\rr_3 = dr \,\rhat \end{equation} leading to \begin{equation} \dV = r^2 \sin\theta \,dr \,d\theta \,d\phi \end{equation} as expected. For any orthogonal coordinate system, this method is of course equivalent to visualizing a small coordinate box, and multiplying the lengths of the three sides.