Let be the portion of the upper-half of the sphere²+²+²=2 outside the cylinder²+²=1in the region with0. In other words,

={(,,):²+²+²=2, ²+²1, 0, 0}.

(a) Use spherical coordinates to find a parametrization (,)for. Write down the normal field=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

(c) Consider a fluid with density

y M(x, y, Z) x2 + y2 + z2Uv . N dS M