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Volume enclosed by a cone and a plane

  1. Apr 20, 2014 #1
    1. The problem statement, all variables and given/known data
    Find the volume enclosed by the cone x[itex]^{2}[/itex]+y[itex]^{2}[/itex]=z[itex]^{2}[/itex]
    and the plane 2z-y-2=0.



    2. Relevant equations
    [itex]\int\int\int[/itex] dV

    3. The attempt at a solution
    In the image Cono=Cone and Plano=Plane

    2expuz6.png
     
  2. jcsd
  3. Apr 20, 2014 #2

    Mark44

    Staff: Mentor

    Problems about integration should be posted in the Calculus & Beyond section, not in the Precalculus section. I have moved your post.
     
  4. Apr 21, 2014 #3
    I have tried to solve it in a different way but I do not think it is much better. Can anybody help me?

    5489c3.png
     
  5. Apr 21, 2014 #4

    LCKurtz

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    For what it's worth, I don't see anything obviously wrong with your work. I entered the ##r,\theta## integral you get into Maple and it just hung trying to solve it. I doubt you are going to find an elementary solution.
     
  6. Apr 21, 2014 #5
    So my first attempt is OK? Because I'm finding troubles with the absolute value of (y) and (-y). I'm not sure if everything I've put is correct.
     
  7. Apr 21, 2014 #6

    LCKurtz

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    I didn't check your rectangular coordinate version. The ##r,\theta## change of variables you used would be the natural way to set it up and that's all I looked at.
     
  8. Apr 21, 2014 #7
    If you do not mind could you please take a look at my rectangular coordinate version?
     
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