It has one.
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An empty cone (like an ice-cream cone) doesn't have any flat surfaces. It has two curved surfaces, one outside and one inside. A solid cone has a flat base, and one other curved surface.
a cone...
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A prism is an elongated 2D shape, while a cone is elongated, just shrinking as it gets to the tip. A cone has a curved surface, while a prism is composed of flat surfaces.
2 flat surfaces unless it is rolled up in which case it has 2 curved surfaces.