## Area and Volume Elements in Cylindrical Coordinates

We can find a volume element in cylindrical coordinates by approximating a cuboid as shown.

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
$d \phi \; dz \rightarrow 0$
.