1. The problem statement, all variables and given/known data Find the center of mass of a circular conical surface (empty cone) of height H. 2. Relevant equations z(CM) = 1/M * int(z*dm) x(CM)=y(CM)=0 (we've taken the origin of coordinates at the center of the base) 3. The attempt at a solution This problem far exceeds my mathematical knowledge so I'll probably be talking nonsense but... here it goes: let L be the slant height of the cone, R the radius of the circular base dm= (M/pi*R*L)*dS dS= 2pi*r*dz (where r is the "radius of each dS", r= R(H-z)/H) We can now solve the integral, obtaining: z(CM)= H^2/3L But, given the problem wording, z(CM) should depend only upon H...! Thank you for your help (and excuse my lousy English)!!!