I'm trying to find the volume and surface area of a 1-D dimensional sphere, i.e. retaining only the radial dependence.(adsbygoogle = window.adsbygoogle || []).push({});

I know that the volume element for a 3-D sphere would be

[tex]dV = r^2\sin\theta{d}\theta{d}\phi{d}r[/tex]

If it's one-dimensional would it just be [tex] dV = r^2{d}r[/tex]? Or would it just be [tex]dr[/tex]?

With regards to the surface area vector in 3-D it is

[tex]d\boldsymbol{A} = r^2\sin\theta{d}\theta{d}\phi\hat{\boldsymbol{e}_r}[/tex]

so in 1-D would it be

[tex]d\boldsymbol{A} = r^2\hat{\boldsymbol{e}_r}[/tex] or would it just be [tex]\hat{\boldsymbol{e}_r}[/tex]?

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.

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# Area vectors for 1-D sphere

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