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Finding the center of gravity/mass of half of an empty cylindrical shell
Forgive me, but you lost me when you began calculating h2. Here is where my mind is: Why is it necessary to calculate a moment? What does dividing "the moment about the x-axis by the circumference of the rounded part of the semicircle" do? Maybe you can tell from these questions where/why I'm not understanding the big picture. Thanks!
Comparing and contrasting equations and functions
I don't see how your answer for d is explained by your answer for b. Wouldn't having a polynomial equal a constant be an equation, which would mean that only some values would satisfy/solve the equation? I asked the question the way I did to try to get clarification on the wording of the text I quoted from the linked post. Specifically where he says that a line parallel with the z axis would not intersect the surface exactly once for f(x,y,z)=const., but it would for z=f(x,y).