$\text { Find the average value of } f ( x , y , z ) = x + y + z \text { over the region } Q \text {, where } Q \text { is a }$

Multiple Choice

$\text { Find the average value of } f ( x , y , z ) = x + y + z \text { over the region } Q \text {, where } Q \text { is a }$ tetrahedron in the first octant with vertices $( 0,0,0 ) , ( 18,0,0 ) , ( 0,18,0 )$ and $( 0,0,18 )$ . The average value of a continuous function $f ( x , y , z )$ over a solid region $Q$ is $\frac{1}{V} \iiint_{Q} f(x, y, z) d V$ , where $V$ is the volume of the solid region $Q$ .

A) $\frac { 55 } { 6 }$
B) $\frac { 54 } { 7 }$
C) $\frac { 54 } { 5 }$
D) $\frac { 27 } { 2 }$
E) $\frac { 55 } { 4 }$