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Volume of wedge

  1. Aug 15, 2012 #1
    1. The problem statement, all variables and given/known data

    The problem is attached in the picture.



    3. The attempt at a solution

    What bothers me is that they say the wedge is bounded by x + z = a. Doesn't this imply that the calculated volume should only be half of what is written in the answers? I'm aware that the plane x + z = a can refer to either the left (negative) side or the right (positive) side. Do we choose one or simply take both?

    Limits for x: 0 to a
    Limits for y: 0 to √4ax
    Limits for z: 0 to a-x


    However, in http://mathworld.wolfram.com/CylindricalWedge.html the wedge is given as the full volume.
     

    Attached Files:

  2. jcsd
  3. Aug 15, 2012 #2
    You have two possibilities: if a>0, then x>0 and z>0. If a<0, then also x<0 and z<0. No value of a works for both regions.
     
  4. Aug 15, 2012 #3

    LCKurtz

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    Assuming ##a>0##, the slanted plane is the "roof" of the solid. I see no reason to limit ##y## to only being positive.
     
  5. Aug 16, 2012 #4
    I see! I initially thought that the x + z = a plane refers to the vertical plane i.e. the x-z plane. But now that you mention it, it actually refers to the plane that is sloping downwards from z = a to x = a, like a ramp.
     
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