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Center of mass of a cone

  1. Nov 2, 2006 #1
    Find the location of the CM of a hollow ice cream cone, with base radius R and height h, and uniform mass denisty. How does your answer change if the cone is solid, instead of hollow?

    Okay, so I'm pretty sure that I need to work with slices, and that you need the mass which I believe is [where sigma is density]

    σ ( (pi) r^2 + (pi) r √r2 + h2)

    Though I don't know where to go from here
  2. jcsd
  3. Nov 2, 2006 #2
    Nm, I think I got it, I have:

    [h^2]/[(3)(R+sqrt(R^2 + H^2))]

    and for the filled cone:

  4. Nov 2, 2006 #3


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    [tex]\vec{R}_{CM}=\frac{\int_A\sigma\vec{r}dA}{\int_A\sigma dA}[/tex]

    Notice that the angle that the cone makes with its symetry axis is [itex]\tan\theta=R/h[/itex]. I leave it to you to evaluate the integrals.
  5. Nov 2, 2006 #4


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    The first one looks far too complicated. What is H anyway? Is that where the CM is located? The filled cone looks good.
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