1. (i) Find the volume V of the solid bounded by y = z? and by the planes y + z = 4 and z = 0 by setting up a triple integral with z as the innermost variable. (ii) Set up a triple integral for finding the volume of the above solid with the innermost variable as r. 2. Change the equation from cylindrical to rectangular coordinates and sketch the graphs in the ryz-coordinate system: (i) z = 4r? and (ii) r = 4 sin 0. 3. (i) A solid E lies between the paraboloid z = 24 - x2 - y? and the cone z = 2vx2 + y?. Using cylindrical coordinates, find volume of E. (ii) Set up triple integrals to find the centroid of E (i.e., center of mass if the density is a constant). 4. (i) If a point P is given by (1, v3,2v3) in rectangular coordinates, find spherical and cylindrical coordinates for it. (ii) Find an equation in spherical coordinates for z = 23 + y?. (iii) Change the equation p = 2 sin o cos 0 to rectangular coordinates, and describe its graph