1. The problem statement, all variables and given/known data Show that a hollow cylinder of radius R_1, outer radius R_2, and mass M, is I=1/2M(R_1^2+R_2^2) if the rotation axis is through the center along the axis of symmetry. 2. Relevant equations $$dm = \rho dV$$ $$dV = (2 \pi R)(dR)(h)$$ 3. The attempt at a solution I was mainly confused about why dV is expressed as (2piR)(dR)(h) since the Volume of a cylinder is 2pir^2h. I know that the variable of integration is R so there has to be a dR in there somewhere, but I'm having trouble understanding the rationale.