Start with \(d\vec{r}\) in rectangular, cylindrical, and spherical
coordinates. Use these expressions to write the scalar area elements \(dA\) (for different coordinate equals constant surfaces) and the volume element \(d\tau\). It might help you to think of the following surfaces: The various sides of a rectangular box, a finite cylinder with a top and a bottom, a half cylinder, and a hemisphere with both a curved and a flat side, and a cone.

Rectangular:
\begin{align}
dA&=\\
d\tau&=
\end{align}
 Cylindrical:
\begin{align}
dA&=\\
d\tau&=
\end{align}

Spherical:
\begin{align}
dA&=\\
d\tau&=
\end{align}