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  
\[ d \phi \; dz \rightarrow 0\]

Add comment

Security code