The Motion of a Liquid in a Cylindrical Container of Radius

Multiple Choice

The motion of a liquid in a cylindrical container of radius 1 is described by the velocity field $\mathbf { F } ( x , y , z ) = - 8 z \mathbf { i } + 2 y \mathbf { k }$ . Find $\iint _ { S } ( \operatorname { curl } \mathbf { F } ) \cdot \mathbf { N } d S$ , where $S$ is the upper surface of the cylindrical container.

A) $- 7$
B) $- 2$
C) 9
D) 0
E) 4