Area and Volume Elements in Cylindrical Coordinates
The cube has sides
\[dR, \; R d \phi , \; dz\]at right angles, so the volume of the cuboid
\[dV \simeq R dR d \phi dz\].
The approximation becomes better as
\[dR, \; d \phi \; dz \rightarrow 0\].
We can also approximate an element of surface area as the area of a rectangle of base and height
\[R d \phi ,dz\]respectively so
\[dA \simeq R d \phi dz\].
Again the approximation improves as
\[ d \phi \; dz \rightarrow 0\].