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

$\displaystyle dV = r^2\sin\theta{d}\theta{d}\phi{d}{r}$

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.