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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.




    x=psin(phi)cos(theta)
    y=psin(phi)sin(theta)
    z=pcos(phi)




    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

    LCKurtz

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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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