I haven't looked at the solution. This is what I'm thinking:

  At first it seems that the problem is not solvable because there's too
little info. We only know that the height of the shape is 6m, but we do
not know the radius of the hole nor the radius of the sphere. These two
radii could be anything, and still the resulting object could be 6m tall.

  But then the problem states that the problem is solvable. I have to
believe that this is true.

  If the problem is solvable, the only conclusion is that the volume of
the shape is *not* dependent on the radii of the cylinder and the
sphere. In other words, changing the radius of the cylinder and the
sphere in such a way that the CSG shape is still 6m tall will keep the
volume the same.

  If this is so then this should be so even if the radius of the
cylinder is 0, in which case the height of the sphere must be 6m
(because that's how tall the CSG shape must be).

  Thus the problem is reduced to calculating the trivial volume of a
sphere of diameter of 6m, which should be something like pi*r^3*4/3 =
pi*3^3*4/3 = pi*36.

  Is this correct?

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