Suppose That $f ( x , y , z ) = g \left( \sqrt { x ^ { 2 } + y ^ { 2 } + z ^ { 2 } } \right)$

Multiple Choice

Suppose that $f ( x , y , z ) = g \left( \sqrt { x ^ { 2 } + y ^ { 2 } + z ^ { 2 } } \right)$ where $g$ is a function of one variable such that $g ( 6 ) = 2$ .
Evaluate $\iint _ { S } f ( x , y , z ) d S$ where $S$ is the sphere $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 36$

A) $368 \pi$
B) $408 \pi$
C) $308 \pi$
D) $288 \pi$
E) None of these