cone; circle is the base
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The lateral area is the surface area of a 3D figure, excluding the area of any bases. For the lateral area of a cylinder, you would take the circumference of the base multiplied by the height of the cylinder to get the lateral area of the surface. It's basically splitting a can down one side, cutting the ends off completely, rolling it out flat, and figuring out the area of the resulting rectangle.
A cone has a round base and a narrowing round top. I hope this answers your question!
A cone is a figure that contains 2 faces and 1 corner. The faces are the base and that slanted surface wrapped around the base. The corner is the apex of the slanted surface.
A sphere has one surface that's also curved and has no base.
An ice cream cone can be approximated as a cone, which has one circular face at the base, one curved face forming the lateral surface, and no top face. It has one vertex at the tip of the cone where the lateral face meets the base. The base circle has one edge, and the lateral face has an infinite number of edges since it is a curved surface without straight edges.