Recently, I was calculating the volume of a sphere with a hole through the center. I started thinking, what if the hole was off-center by some distance e. I have searched high and low and can not find anything on this situation. I have tried calculating, but after the second integral, I can not complete the third (due to complexities of the equation).(adsbygoogle = window.adsbygoogle || []).push({});

I have found the special case of Viviani's Curve, whereby e is equal to half the hole radius, and the hole radius is half the sphere radius, but that does not help.

I know this can be solved numerically (or through a CAD program), but I'm determined to try and find an analytical solution. Has anybody come across information that may help? I can post some equations if necessary.

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# Sphere with a non-centered hole

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