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Triple integral to find Volume of Solid

  1. Sep 12, 2010 #1
    1. The problem statement, all variables and given/known data
    Use a triple integral to find the volume of solid enclosed between the sphere and paraboloid.


    2. Relevant equations
    Equation for sphere x2+y2+z2=2a2
    Equation for paraboloid az = x2+y2 (a>0)

    3. The attempt at a solution
    Trying to find limits of integration:
    For integration of dz, rearranging the both equation in terms of z, the limits are from
    z= 1/a (x2+y2) to
    z= SQRT (2a2 - x2 - y2)

    Next i suppose i should find the equations in xy plane by solving the given equations simultaneously to determine where the sphere and paraboloid intersect. When i equate both equation, i got this expression
    2a4= (x2+y2)2+a2(x2+y2). I got stuck here as I do not know how to find the limits for dx and dy. Do i need to use polar coordinates or sphere coordinates? Can anyone explain these to me? Thanks
     
  2. jcsd
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