Find the location of the CM of a hollow ice cream cone

[Tonyt88]

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

 

[Tonyt88]

Nm, I think I got it, I have:

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

and for the filled cone:

h/4

 

[quasar987]

\vec{R}_{CM}=\frac{\int_A\sigma\vec{r}dA}{\int_A\sigma dA}

Notice that the angle that the cone makes with its symetry axis is \tan\theta=R/h. I leave it to you to evaluate the integrals.

 

[OlderDan]

Nm, I think I got it, I have:

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

and for the filled cone:

h/4

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