text: centre of mass of hollow cone??? what is the centre of mass of hollow cone. if you want a proof, here's one by calculus when the cone is positioned upright, standing on its tip we can find the center of mass by the formulas  x' = ∫(x*da)/∫(da)  y' = ∫(y*da)/∫(da)  ---with the limits from  x = 0 to x = b(base)   y = 0 to y = h(height)  by intuition center of mass along x = 0  we can represent the equation of the cone as y = mx, where m is the slope  so finding the center of mass along y we find ∫yda = ∫y*2πxdy, since da=2πxdy from infinitesimal area a = 2πrh  = 2π∫(y^2)dy/m  = 2π(y^3)/3m evaluated from 0 to h  = 2πh^3/3m, we can find m from y = mx ---> h = mb so m=h/b  = 2πb(h^2)/3  then we have to find ∫da ∫da = ∫2πxdy  = ∫2πydy / m  = π(h^2)/m  = πbh  so y' = ∫(y*da)/∫(da) = 2πb(h^2)/3πbh = 2h/3 this means the center of mass along the vertical axis of the cone is 2h/3 when the cone is standing on its tip y = 2h/3 and x = 0