So like you guys are mentioning above you can also build this shape by building just a starting surface and then extruding it - if you extrude a surface you will always get caps on it since it can be capped just by copying the potentially non-planar surface to the other side.

But I would encourage you to think more along the lines of slicing a base solid like I showed above, because it's a lot more general purpose and you will generally use that same process to take other kinds of cuts out of the object as well like slicing it by side profiles.

If you did want to do it by extruding a surface you don't need to use curve projection as a separate step because Trim already has projection built into it, so just trim the sphere directly with your 2D profiles, then extrude the trimmed sphere surface piece.

- Michael