Need help with a through c, the problem is complete! no graph or extra material

3) Let M be the portion of the upper-half of the sphere x2 + y2 + 22 = 2 outside the cylinder x2 + y? = 1 in the region with y 2 0. In other words, M = {(x, y, z) : 2 + 2 + 2 = 2, 22 + y 2 1, y 2 0, z 2 0}. (a) Use spherical coordinates to find a parametrization & (, 0) for M. Write down the normal field & x Do associated with your parametrization and indicate whether this normal field is outward or inward. (b) Use your parametrization in (a) to find the area of M. (c) Consider a fluid with density M(x, y, z) = lyl 2 2 + 92 + 22 measured in g/ in' flowing with velocity v(x, y, z) = (0, a, 1) measured in in / s. Show that the amount of fluid that passes through our surface M going towards the origin after 3seconds is 3 Mv . NaS = 1 -2V2, where N is a vector field consisting of inward normal vectors to M. (d) Note that the quantity in (c) is a negative number. What is the physical meaning of this negative sign