The question: "Find the average z-value of points in the ice cream cone shaped region common to the sphere x^{2}+ y^{2}+ z^{2}= 4 and the cone z = sqrt(3(x^{2}+ y^{2})). I know how to find the "average value" of a function, but I don't quite understand what my professor wants when she says the "average z-value".

For those who might need to know for some reason, I did find the volume of "ice cream cone shaped region" which she has mentioned:

Note: I used spherical co-ordinates (and I'm fairly sure I'm right)

-Giest