The Surface Integral $\int \int$ S $z ^ { 2 } d S$

Multiple Choice

The surface integral $\int \int$ S $z ^ { 2 } d S$ where S is $z ^ { 2 } = x ^ { 2 } + y ^ { 2 }$ between $z = 1$ and $z = 2$ is

A) $- \frac { 15 \pi } { \sqrt { 2 } }$
B) $\frac { 15 \pi } { \sqrt { 2 } }$
C) $\frac { 15 \pi } { \sqrt { 3 } }$
D) $- \frac { 15 \pi } { \sqrt { 3 } }$
E) $\frac { 15 \pi } { 2 }$