what is the centre of mass of a 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*2pxdy, since da=2pxdy from infinitesimal area A= 2prh = 2p?(y^2)dy/m = 2p(y^3)/3m evaluated from 0 to h = 2ph^3/3m, we can find m from y= mx --- h= mb so m=h/b = 2pb(h^2)/3 then we have to find ?da ?da= ?2pxdy = ?2pydy/ m = p(h^2)/m = pbh so y'= ?(y*da)/?(da)= 2pb(h^2)/3pbh= 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