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Finding the Mass of a Solid in 3d

  1. Nov 25, 2011 #1
    1. The problem statement, all variables and given/known data
    Find the mass of the solid bounded by the cylinder [itex]x^2+y^2=2x[/itex] and the cone [itex]z^2=x^2+y^2[/itex] if the density is [itex]\delta = \sqrt{x^2+y^2}[/itex]

    [b2. The attempt at a solution[/b]
    I had some trouble looking at how to set up the limits on this integral. What I came up with was:
    [itex]2 \int_0^2 \int_0^{\sqrt{2x^2+2x}} \int_0^{\sqrt{x^2+y^2}} \sqrt{x^2+y^2} dzdydx [/itex]
    [itex]= 2 \int_0^2 x^2\sqrt{x^2+y^2} + ((\sqrt{x^2+y^2})^3)/3 dx[/itex]
    And this is just an ugly integral. I tried doing it in cylindrical coordinates but it wasn't working out terribly well that way either. Any hints? Thanks!
     
  2. jcsd
  3. Nov 25, 2011 #2
    Nevermind, I got an answer. Can anyone confirm [itex]6\pi[/itex]?
     
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