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Centroid of a half cone

  1. Jan 30, 2008 #1
    The question is this: find the centroid of the half-cone
    sqrt(x^2 + y^2) <(oet) z <(oet) 1
    and x >(oet) 0
    (oet being or equal to, I apologize for the lack of sophistocated symbols). I thought I was doing it correctly, but my answers do not match up with those in the book.

    I assumed that it would be wise to use cylindrical coordinates which would make r <(oet) 1 and z <(oet) 1. Now, for the limits of integration, I used

    0 < r < 1,
    -pi/2 < theta < pi/2 and
    0 < z < 1.

    The mass is the triple integral of [r dr dtheta dz]. And to find the centroid coordinates I take the triple integral of my particular coordinate multiplied by r and over the mass. I'm pretty sure I know how to integrate, so I assume that my mistake was in my limits or perhaps my choice of coordinate system.

    Advice please and thank you....

    Wakko. =)
  2. jcsd
  3. Jan 30, 2008 #2


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    It doesn't sound like you are doing anything obviously wrong. Maybe you could post your result and let people check it.
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