1. The problem statement, all variables and given/known data Here is the surface I need to parameterize. It is a solid of revolution. 2. Relevant equations 3. The attempt at a solution So since its a piecewise function, I can define it as follows (x-2)^2 + z^2 = 1, 1<x<2 z = -x+3, 2<x<3 z = x-3, 2<x<3 I know the formula for the area for a solid of revolution, but how do I parameterize this surface and then use that to calculate the surface area? I'm lost.