Centroid of cylindrical cone

  1. 1. The problem statement, all variables and given/known data

    Determine the centroid of volume for a right circular cone with base diameter of 100mm and an altitude of 200mm.

    2. Relevant equations

    I know that if the my xy-plane is parallel to the base of the cylindrical cone then the x and y coordinates of the centroid must be zero and therefore I only need to find the z coordinate of the centroid.

    The equation I am using is

    [tex]z_c = \frac{1}{M} \int_{body} z dm[/tex]

    where M is the total mass and [tex]dm = \rho dV[/tex]

    3. The attempt at a solution

    I am trying to use cylindrical coordinates but I think my limits of integration are incorrect. I have tried to solve the integral above with the following limits.

    [tex]0<\theta<2\pi [/tex]

    [tex]0<r<50 [/tex]


    I'm not sure if the limits for the z coordinate is correct. Am I on the right path?
  2. jcsd
  3. LowlyPion

    LowlyPion 5,324
    Homework Helper

    Well, I wouldn't worry with polar coordinates, because you are dealing with basically a stack of disks aren't you?

    They are each have a weight of ρ*πr²

    Exploit then the fact that r is a function of z, and your integral should be pretty straight forward shouldn't it?
  4. Thank you. I was essentially doing the right thing on my first try before I changed everything, but I made an algebra mistake when trying to use cylindrical coordinates. Thanks for the short cut ... less room for stupid mistakes.
Know someone interested in this topic? Share this thead via email, Google+, Twitter, or Facebook

Have something to add?
Similar discussions for: Centroid of cylindrical cone