This question was posed to me by a friend, so I’m consulting my expert systems on it. =)
Basically, assume you cut a cone from a sphere, leaving a pointy-topped cone with a rounded bottom. Is there a specific name for this shape?
Math / Geometry majors, attack!
MathWorld calls it a spherical cone.
How can you cut anything with a “pointy top” from a sphere?
There is a whole set of geometric shapes called Conic Sections, which are defined by the intersection of planes (at various angles) and a sphere.
Oops. Intersection of planes and a CONE (not sphere).
What’s the name for a conic slice from a sphere?
A bad design for a beer bottle.
Spherical Cone looks like the answer of choice… after all, who’s to argue with Wolfram when it comes to math. =)
Well I did send him an email over the summer telling him to get his act together regarding ordinal operations, but no update so far. 
If I understand the OP correctly, it would be the piece removed from this sphere.
