$\mathbf { F } = | r | r$ , Where

Multiple Choice

$\mathbf { F } = | r | r$ , where $r = x \mathbf { i } + y \mathbf { j } + z \mathbf { k } , S$ consists of the hemisphere $z = \sqrt { 3 - x ^ { 2 } - y ^ { 2 } }$ and the disk $x ^ { 2 } + y ^ { 2 } \leq 3$ in the $x y$ -plane. Select the correct answer.

A) $20 \pi$
B) $22 \pi$
C) $21 \pi$
D) $18 \pi$
E) $19 \pi$