Finding volumes from infinitesimal displacements

  • Thread starter Niles
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  • #1
Niles
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Homework Statement


In spherical polar coordinates, the infinitesimal displacement ds is given by:

[tex]
ds^2 = dr^2 + r^2 d\theta ^2 + r^2 \sin \left( \theta \right)^2 d\phi ^2
[/tex]

Can I find the volume of a sphere using ds?

The Attempt at a Solution


I know the spherical volume-element is given by [tex]dV = r^2 \sin \left( \theta \right)drd\theta d\phi[/tex].

I can always make a figure showing the geometry of spherical coordinates, but is there a general way of finding the volume from ds? Perhaps finding the area, and then the volume?
 
Last edited:

Answers and Replies

  • #2
Niles
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No hints at all?

I thought of ds^3, but ds is a vector, so that won't work.
 

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