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Homework Help: Finding the Volume of a tetrahedron using Spherical Coordinates

  1. Nov 16, 2009 #1
    Find the volume of a tetrahedron under a plane with equation 3x + 2y + z = 6 and in the first octant. Use spherical coordinates only. The answer is six.


    I've been trying to figure out the boundaries of this particular problem all night. To be honest, I'm completely at a loss. I have p going between 0 and (6/(cos(phi)+sin(phi)(3cos(theta)-2sin(theta)). I believe that theta is between 0 and pi/2, although I'm not entierly sure on that one. As far as phi goes I believe the upper limit is pi but the lower limit is a mystery to me.
  2. jcsd
  3. Nov 16, 2009 #2


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    [itex]\phi[/itex] would go from 0 to [itex]\pi/2[/itex] as does [itex]\theta[/itex].
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