How to make a recess in a sphere normal?

Question

Blender

Hello. Faced a problem. We have a UV sphere and a cone.
Task: Make a recess in the sphere in the form of a cone. It would seem that it is complicated, but I am a beginner and still do not quite know all the features. What do I do and what happens.
Using the Boolean - Difference modifier, I make an incision in the sphere. Then I align the vertices with respect to the Y axis so that they are in the same plane. It turns out pretty good.
But next I need to smooth this sphere with Shade Smooth + Subdivision Surface modifier. And it doesn't turn out very nice.
Question. What methods to correct these irregularities? Maybe there is another way to create an incision in a sphere. Or maybe I'm missing something. Tell me please.

Answer 1

If the angle between the outer and inner parts of the sphere should remain unsmoothed - press ALT + N in the sphere editing mode and select the Average item, in it - Corner Angle. The edge of the cut will highlight in cyan and will appear unsmoothed in volumetric mode.