Evaluate $\iint _ { S } f ( x , y , z ) d S$

Multiple Choice

Evaluate $\iint _ { S } f ( x , y , z ) d S$ . $f ( x , y , z ) = 5 x + 6 y + z$ ; S is the part of the cone $z = \sqrt { x ^ { 2 } + y ^ { 2 } }$ between the planes $z = 1$ and $z = 4$ .

A) $126 \pi \sqrt { 2 }$
B) $42$ $\pi \sqrt { 2 }$
C) $126 \sqrt { 2 }$
D) 0