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Patch of a surface in spherical coordinates?

  1. Mar 16, 2013 #1
    1. The problem statement, all variables and given/known data
    I am currently trying to prove:

    S = ∫∫a2sinΦdΦdθ

    Here is my work (note that in my work I use dS instead of S, this is an accident):
    92zNaWh.jpg

    I end up with:

    S = ∫∫a*da2sinΦdΦdθ

    Where da is the infinitesimal thickness of the surface.

    Why am I getting the wrong answer?
     
  2. jcsd
  3. Mar 16, 2013 #2

    Dick

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    You haven't computed S. You've computed the volume V=S*da. To get S, divide by the da.
     
  4. Mar 16, 2013 #3
    I thought that if the volumetric shell thickness approaches zero you end up with the surface area?
     
  5. Mar 16, 2013 #4

    Dick

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    If the shell thickness approaches zero then you end up with zero volume. To get the surface area divide by the thickness as it approaches zero. Maybe that's what 'volumetric shell' means.
     
    Last edited: Mar 16, 2013
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