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.
a cone
Cone
A pyramid has 5 flat surfaces, 4 for the walls and 1 for the bottom.
Cone....
you are a cone
A cone !!
Cone
A sphere.
a hemisphere. a cone. i'm sure there are others as well.
This is an impossibility. If it is a solid figure then it will have more than 1 surface. If it has only 1surface and it is a solid, then it must be a sphere, but the surface of a sphere is not flat is it? By using the word 'solid' then by definition, it is three dimensional and has thickness. A cylinder has no vertices , but it has 2flat surfaces. A vertex is a point where three lines meet, such as on a pyramid, which has 4 vertices. Have I forgotten something or is this a 'trick' question?
The description given fits that of a cone.
A cone has 1 flat surface, because a cone has 1 corner and has 4 edges. The reason that is is because a cone is round. A cone has a flat surface at the bottom of the cone. The reason it is because the cone doesn't have any vertices and most of the solid and plane figures have vertices.
Cylinder
Cylinder
If you mean 1 flat surface and 1 vertex, then the only thing I can think of is a cone.
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.