A cone can be thought of as a pyramid with an infinite number of faces. In the figure below, keep clicking on 'more' and see that as the number of faces increases, the pyramid begins to look more and more like a cone.
In the limit, as the number of faces approaches infinity, the shape is a cone.
Cones and pyramids both have the same way of calculating volume. In both cases the volume is one third of the base area times the height:
For more on this see Volume of a cone and Volume of a pyramid.