A cone is a solid that has a circular base and a a single vertex. If the vertex is over the center of the base, it is called a right cone. If it is not, it is called an oblique cone. An object that is shaped like a cone is said to be 'conical'.
The volume of a cone is given by the formula where r is the radius of the circular base, and h is the height - the perpendicular distance from the base to the vertex.
For more on this see Volume of a cone
The surface area of a cone is given by the formula
For more, see Surface area of a cone
Another way to think of a cone is as a pyramid with an infinite number of faces.
For more on this see Similarity of cones and pyramids.