Ok, seems like you guys are in agreement with the fillet/trim, would that work under the following circumstance.....

I'm looking to extrude the circular edges out from the cut peices so I would end up with something that would look like an old WW2 shipping mine, or something in the attached photo. I looking for a really nice crisp line between the curve of the sphere and the jutting out of the pipe.

I know I could just have a curve and a pipe intersecting, but I dont think that would look to go really, or am I wrong?

Sorry for the poor ref pic btw, first one i could come up with in google