Differential Volume in Cylindrical Coordinates
Formulas
The infinitesimal volume in spherical coordinates is given by:
$$ dV=r^{2}\sin\theta dr d\theta d\phi $$
The infinitesimal surface area on a sphere can be obtained without multiplying $dr$ by:
$$ da=\color{blue}{rd\theta} \cdot \color{red}{r\sin\theta d \phi}=r^{2}\sin\theta d\theta d\phi $$