The motion of a solid object can be analyzed by thinking of the mass as concentrated at a single point, the center of mass. if the object has density rho(x, y,z) at the point (x, y,z) and occupies a region w, then the coordinates (x, y,z) of the center of mass are given by

m jw im

assume x, y, z are in cm. let c be a solid cone with both height and radius 3 and contained between the surfaces z=sqrt{x^2+y^2} and z=3. if c has constant mass density of 2 g/cm^3, find the z-coordinate of c's center of mass.