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Example on spherical coord. and trip. integral

  1. Nov 29, 2007 #1
    [SOLVED] Example on spherical coord. and trip. integral

    1. The problem statement, all variables and given/known data

    Here's the example in the book. They're proving the volume of a sphere using spherical coordinates.

    A solid ball T (the region) with constant density [tex]\delta[/tex] is bounded by the spherical surface with equation [tex]\rho = a[/tex]. Use spherical coordinates to compute its volume V.

    It says that the bounds are:

    [tex]0 \leq \rho \leq a, 0 \leq \phi \leq \pi, 0 \leq \theta \leq 2 \pi[/tex]

    The bounds for [tex]\phi[/tex] confuse me. Why does it go from 0 to pi? Wouldn't that only account for half of the sphere?

    Any help is appreciated.
     
  2. jcsd
  3. Nov 29, 2007 #2

    Dick

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    One angular coordinate measures pole to pole angle, that goes from 0 to pi. The other measures the equatorial angle, that goes 0 to 2pi. Together they cover the whole sphere.
     
  4. Nov 30, 2007 #3

    HallsofIvy

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    Draw a picture. If [itex]\phi> \pi[/itex] you would be picking up the same points as with [itex]\phi< \pi[/itex], [itex]\theta> \pi[/itex].
     
  5. Nov 30, 2007 #4
    Oh ok, I get it, as theta goes from 0 to 2pi, phi sweeps the entire sphere. Thank you both.
     
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