I've been unable to find the geometric name for the following shape, does one exist?
[Math] the name of this geometric shape – A Cylinder with a Cone Atop
geometryterminology
Related Solutions
The surface is a "circular paraboloid" (a special case of the "elliptic paraboloid"). Slices by planes perpendicular to the $z$ axis are (concentric) circles, while slices by planes parallel to the $z$ axis are (identical) parabolas.
It's an example of a surface of revolution, in this case obtained by revolving the basic parabola shape (think $y = x^2$) about its axis.
The filled counterpart would simply be a "solid circular paraboloid".
Best Answer
Can't find anything better than "Cylindro-conical shape". However, a pyramid on top of a prism is called "elongated pyramid". If we can apply similarity then this shape should be called "elongated cone".