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The average value of a function
f(x, y, z) over a solid region E is defined to be
fave = 1/V(E) Ef(x, y, z) dVwhere V(E) is the volume of E. For instance, if is a density function, then ave is the average density of E.

Find the average value of the function
f(x, y, z) = 5x2z + 5y2z
over the region enclosed by the paraboloid
z = 4 − x2 − y2 and the plane z = 0.



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