Hi, I am working through the Feynman lectures on physics and trying to calculate the moment of inertia stated in the title. (the taxis of rotation going through c.m., orthogonal to length). My approach is to slice the cylinder into thin rods along the length, using the parallel taxis theorem and the result for a rod. Unfortunately, I get as result: I = M ( L^2 / 12 + r^2 / 2). I.e. the last numerator comes out as 2 instead of 4, as stated in section 19-2. The corresponding expression comes from summing up dm sum( z_i ^ 2), where dm is the mass of a single rod and z_i the height of the rod's center of inertia. Perhaps my mistake lies in handling the 2-dim slices as 3-dim rods?