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I don't think there is a special name for that.

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It is a nappe of a cone.

Q: What is name of half of a right circular cone?

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A 2d cone is called a Light Cone. <edit: Isn't it called a circle sector?>

A cone could be a party hat && a sphere couldd be a bowling ball.

That would be an inverted cone...

solid with 1 edge is a cone .

It can also be called a circular graph

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edge-Apex

that would be a cone.

It's A CONE

A cinder cone volcano

I'm assuming you are looking for the name of the conic section produced by this type of intersection? If a right circular cone is intersected by a plane parallel to one edge of the cone, the resulting curve of intersection would be a parabola. If the intersecting plane was parallel to the base, it would be a circle. If the intersecting plane was at any angle between being parallel to the base and being parallel to an edge, it would produce an ellipse or part of an ellipse (depending on whether the intersection was completely within the cone).

It is the vertex. It can also be called the apex but that has a connotation of being the top-most point and so is not appropriate when both nappes are concerned.

A semi-circular driveway.

A sphere intersected by a plane, An circular ellipsoid intersected by a plane, A cylinder, A cone, and many more shapes, some of which don't even have a name!

A cone+++The original answer also had "Cube", which is obviously wrong!

A 3-D cone would act as the ice cream cone and a 3-D sphere would act as the ball of ice cream.

Dave Cone's birth name is Dave A. Cone.

cone