Find the mass of the lamina that is the portion of the cone z = √x² + y² between z = 1 and z = 4 if the density is p(x,y,z) = x²z. Consider the radial vector field F = (x, y, z). Is the upward flux across the hemisphere x2 + y²+z² = 1, for z> 0, or across the paraboloid - z=1-x2 y2, for z > 0. Note that the two surfaces have the same base in the xy-plane and the same high point, (0, 0, 1). Use an explicit description for the hemisphere and a parametric description for the paraboloid.