I want to connect the cylinder to the half-sphere without changing their positions (they are separate objects with space between them).  In reality the half-sphere and cylinder have a lot more faces than this simplified version.  What is the most elegant way to do this?  The connecting surfaces can be anywhere, as long as they are inside the hemi-sphere.  In the end I want to 3D-print the model so that the cylinder is floating in the hemi-sphere exactly as it is positioned now.

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