I was helping a math undergrad (senior, graduating with honors) from a top 50 university study for the actuarial exam. They were stuck on a question that amounted to "what's the volume of this circular cylinder?"

As I walked them through that, it dawned on me that the problem wasn't recalling or applying the formula, but that they had no idea what x = cos theta, y = sin theta, theta ranges 0 to 2*pi, z ranges 0 to 2 would graph. No idea and no idea how to even begin...