## 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

\[ d \phi \; dz \rightarrow 0\]

.