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Finding volumes from infinitesimal displacements

  1. May 4, 2008 #1
    1. The problem statement, all variables and given/known data
    In spherical polar coordinates, the infinitesimal displacement ds is given by:

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

    Can I find the volume of a sphere using ds?

    3. 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: May 4, 2008
  2. jcsd
  3. May 4, 2008 #2
    No hints at all?

    I thought of ds^3, but ds is a vector, so that wont work.
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