A potter is throwing clay on a wheel which turns at a constant rate. It starts as a solid cylinder of radius r and height h and gradually changes into a jar with the cross-section shown in the diagram.

Assume the mass, M kg, and the density of the clay are constant.
i) Find an expression for the density of the clay.
ii) Find the height, in terms of h, of the jar when the thickness of the base is 0.2h and the inside radius is 0.9r.
iii) Assuming the jar is a solid cylinder with another removed from the inside, find its moment of inertia about its axis of rotation in terms of M and r.
iv) Find the ratio of the kinetic energy of the jar to that of the original cylinder.