SCalcET$815\mathrm{.}6\mathrm{.}508.$XP$.$

The average value of a function

f$($x$,$ y$,$ z$)$

over a solid regionEis defined to be

fave $=$

$1$V$($E$)$

E

f$($x$,$ y$,$ z$)$ dV

where

V$($E$)$

is the volume ofE. For instance, if$$is a density function, then

$$ave

is the average density ofE.

Find the average value of the function

f$($x$,$ y$,$ z$)=5$x$2$z $+5$y$2$z

over the region enclosed by the paraboloid

z $=9$ x$2$ y$2$

and the plane

z $=0.$