A cone of height h and base radius r has density equal to distance from its base. Find it's center of mass. How do I write a function for the density? Is it p=h-z? And what are the limits of r if I want to do this in cylindrical coordinates? Thanks in adv.
Your density p increases with h h is along the z axis. x = rcos(theta), y=rsin(theta) z = z. The density increases with base, so assuming the base sits on the xy plane, your density will just be linear to z. p=z. The Your limit for r I think would just be 0,R since it is an undefined base. Same with height, 0,h