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Two: inside and outside.
The flat and the curved surfaces. In ice cream cone terms the ice cream and the cone are the two surfaces. Even if you eat the ice cream and the cone gets empty there are 2 surfaces, the inside and the outside curved surfaces.
A cone has one side, the bottom surface, but not all cones have this surface. They may also be considered to have 'an inside' and 'an outside', which would be two sides. But as a relative of the circle, a cone has mathematically infinite sides.
a cone has circle at bottom
cone