A line?
a sphere
a sphere
One curved surface (two if it is hollow) and no edges.
a cone.
A curved surface is like imagining a sheet of paper that is bent or a flag waving in the wind. A curved edge is like an elastic stick bent in one(C curve) or more points(S curve). The curved surface beeing 3 dimensional(3D) and the curved edge 2 dimensional(2D) unlike the simple surface and edge which are 2D respectively 1D.
The solid that has one flat face, one curved face, one edge, and one vertex is a cone. The flat face is the circular base, the curved face is the conical surface, the edge is the circular boundary where the base meets the curved surface, and the vertex is the pointed tip of the cone.
A cone. A hemisphere.
cone
A cone.
A Cylinder
The shape of the face on a cone is a circular base at the bottom and a curved surface that narrows smoothly to a point called the apex. This curved surface is referred to as the lateral face of the cone. Overall, a cone has one circular face (the base) and one curved surface.
You are probably thinking of the Moebius strip.