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Homework Help: Triple Integral in Cylindrical Coords

  1. May 3, 2012 #1
    1. The problem statement, all variables and given/known data
    Construct a triple integral in cylindrical coords to find the volume of the cone r=z, where the height (z value) is limited by z=L.
    Should be in the form => {int[b,a] int[d,c] int[f,e]} (r) {dr dtheta dz}
    (Sorry for weird formatting above, brackets purely to make terms more discernible)
    Then evaluate using this order of integration to find volume.

    2. Relevant equations
    Volume of a cone => V=[(pi)(a)^2(L)]/3
    In a cylindrical coord system, r=z describes an inverted cone of infinite height

    3. The attempt at a solution
    Currently working on an attempt, but if someone could help out with the understanding, that would be great. It doesn't immediately make alot of sense to me.
    i.e. r=z gives infinite height, but the volume is limited by L, so how do I find limits for that? Also can't see any immediate limits for theta in this situation.
  2. jcsd
  3. May 4, 2012 #2
    What do you mean? The limits you are given are [itex]0 \ge z \ge L [/itex] and [itex] 0 \ge r \ge z [/itex]. Everything is bounded here. Try drawing a picture to see why the limits are as they are.
  4. May 4, 2012 #3


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    Gold Member

    I think you mean: [itex]0 \le z \le L [/itex] and [itex] 0 \le r \le z [/itex]
  5. May 4, 2012 #4
    Whoops! Indeed L>0 :)
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