1. The problem statement, all variables and given/known data Consider a solid homogeneous object taller than its wide, with the top and bottom parallel. Prove that the shape with the lowest moment of inertia about an axis through the object is a cylinder with the axis through its axis of symmetry. density, mass, and height are constant. 2. Relevant equations ∫p^2dm = I, where p is the radius and dm is the differential of mass. 3. The attempt at a solution Maybe start with a cylinder and show that decreasing the radius of any disc of height dh and increasing the radius of another disc of height dh results in an increase in the moment of inertia? The problem with this question is that it doesn't say anything about how symmetric the shape is.