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