I'm trying to find the volume and surface area of a 1-D dimensional sphere, i.e. retaining only the radial dependence.
I know that the volume element for a 3-D sphere would be
If it's one-dimensional would it just be ? Or would it just be ?
With regards to the surface area vector in 3-D it is
so in 1-D would it be
or would it just be ?
Essentially what I'm trying to do is a Finite Volume Method for a 1-D sphere and I want to find the surface area vectors, and volume for my Finite Volume Cells.