1. Find the surface area of the part of the surface z² = 4x² +4y² lying between z = 0 and z = 2. (a) Find the intersection of the surface z² = 4x²+4y² and z = 2. (b) Graph the surface we are trying to find the area of. (c) Parameterize the surface using cylindrical coordinates to get r(r, 0). Don't forget to include the intervals for the parameters. (d) A rectangle with dimensions Ar and A0 gets mapped by the parameterization onto the surface, to a patch that is roughly a parallelogram. The area of this patch is approximately calculated by the formula AS = Calculate the area AS for this surface. • (e) Find the total surface area by integrating. 4. Suppose the surface of problem 1 has a variable density of p(x, y, z) = √4 — z². Find its total mass. Assume the units of mass are grams, and the units of distance are meters. (a) What are the units of p? = (b) In the previous problem, we calculated the area of a patch as |r, × re| Ar A0 = (c) What is the mass of a patch? (d) Integrate to find the total mass.