Don't know what you mean by offset, but the hole is drilled though the center of the sphere.
Does this hold for offset holes?
I'm neither a mathematician, nor much of a logician. But when I thought of this puzzle, I refused to think on so large of a scale. I imagined a 12" sphere with an offset hole. I imagined the shape that would be drilled out, and considered that 6" length, was that the longest length, the shortest, or the average. At that point I could no longer go on.
Does that help?