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

question 9

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) \(\frac { 55 } { 4 }\)

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