A cone is an infinite surface of revolution generated as shown:

Figure 1: Generating a cone.

The term also refers to the solid bounded by one of the nappes and a flat elliptical base. If in this case the base is circular (at right angles to the axis), the cone is called a right circular cone.

Figure 2: The cone as a solid.

The surface area S (excluding the base) and volume V of a right circular cone are given by

\[ \begin{eqnarray*} S & = & \pi r \sqrt{r^2+h^2} \\ & & \\ V & = & \frac{\pi r^2h}{3} \end{eqnarray*} \]