a and b only.

(6) Let M be the portion of the sphere x2 + y + z? = 9 in the first octant outside the cylinder x2 + y = 1, that is, M = { ( x, y, z) : x2 + y + z = 9, x2 + y 2 1, x 2 0, y 2 0, zz0). (a) Use spherical coordinates to find a parametrization (4, 0) for M. Write down the normal field Po X De 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) = Vx2+ 2+ zz measured in g/in' flowing with velocity U ( x, y, Z) = (y, -x, 1) measured in in/s. Compute net amount of fluid that passes through our surface M going towards the origin after 2 seconds, that is, compute 2 / HU . Nas , where N is a vector field consisting of inward normal vectors to M