1. You are given clues to help you evaluate the differential. The tell you that you have a specefic volume, which means you're volume will be fixed. So we can then say that:
You can solve for H in the equation for volume, and then plug it into the area of a right cone. From there you simply differentiate to obtain the optimum radius that will help you minimize the construction of the cone.
#2 is solved in the same way: determining what the question is asking, gathering necessary equations, and seeing what variables we can eliminate through substitution.