Let S Be the Closed Surface Which Is the Portion $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 4$

Multiple Choice

Let S be the closed surface which is the portion of the sphere $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 4$ with $- 2 \leq \boldsymbol { z } \leq 1$ topped by the disk in the plane $\bar { z } = 1$ , oriented outward.Then the flux of $\vec { r } = x \vec { i } + y \vec { j } + z \vec { k }$ through S is:

A) $9 \pi$
B) $24 \pi$
C) $27 \pi$
D) $18 \pi$
E) $36 \pi$