cones have round bases
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Cones, pyramids, and spheres have.
Similarities: both have a base which extends into a single vertex.Differences: a cone only has 1 edge and a pyramid has a minimum of 6 (for a triangular pyramid).the base of a pyramid is a polygon - the base of a cone is a curve(a mathematical cone has no edges at all it is a continuous sheet - or two sheets if you consider the vertex as dividing the surface into two sheets).
False, prisms can have more than one base.
Cones, pyramids, and spheres don't, and I'll bet I could name even more if I thought about it.
No. You need to have the same vertex angle, or have the same ratio between the height and radius of the cones in order to have similar cones.