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.
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Yes, the circular base at the bottom. Faces are any flat surfaces.
Mathematically, a cone is infinite and so has no flat surface. The popular cone is actually a truncated cone and does have 1 flat surface.
It has one.
one
A cuboid has 6 sides/faces/flat surfaces.