Cerius said:

DieCommie, great solution, but could you please supply information on how you came up with upper+lower boundries, the f(r,thetha)=r^2 as well as the constant part 1/49pi?

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Sure.

The general form to find the height is volume/area.  So what I do is integrate to find the volume and then divide by the area.  First the volume...  I note the circular symmetry so I convert to polar coordinates    Now to find the volume of rotation I first need the area under the curve which is simply .  Then I need to rotate that area about the whole circle, so I integrate this .  Combining these two gives me the integral I had which is the volume.  Now the area is easy, its the areas of the circle, .

I think that covers it.  Feel free to ask if you have other questions, I do this for a living!