Evaluate the Surface Integral $\iint _ { S } z d S$

Multiple Choice

Evaluate the surface integral $\iint _ { S } z d S$ , where S is that part of the cylinder $z = \sqrt { 1 - x ^ { 2 } }$ that lies above the square with vertices $( - 1 , - 1 ) , ( 1 , - 1 ) , ( - 1,1 )$ , and $( 1,1 )$ .

A) $\sqrt { 2 }$
B) $2$
C) $\sqrt { 8 }$
D) $4$
E) $\pi$
F) $2 \pi$
G) $4 \pi$
H) $8 \pi$