1. The problem statement, all variables and given/known data 2. Relevant equations n/a 3. The attempt at a solution 1) Whenever I need to find the volume between two surfaces, the integrand is simply the difference (subtraction) of the two equations? In the solution guide above, it is clear that they subtracted the two equations for z. 2) After transforming the double integral into polar coordinates, how did the solutions guide figure out the limits of integration? The object being integrated is a paraboloid limited by z = 4. Why then do the limits go from 0 to 2pi? Where do the limits for R (the inner integral) come from?