Cone

A cone is a pyramid based on a disk. It is also the solid of revolution of an isosceles triangle around its axis of symmetry. It has a disk for its base and a curved side someitmes called a nap.

Joining two cones at their circular bases produces a bicone.

Coordinates
Where r is the radius of the base and h is the height:

The vertex of a cone is


 * $$\left(0,\,0,\,h\right).$$

Points on the edge of a cone are all points (x,y,0) such that


 * $$x^2+y^2=r^2.$$

Points on the surface of a cone are all points (x,y,z) such that


 * $$\sqrt{x^2+y^2} = r(h-z) \quad\text{and}\quad z>0,$$ (nappe)
 * $$x^2+y^2=r^2 \quad\text{and}\quad z=0.$$ (disk)

Points in the interior of a cone are all points (x,y,z) such that
 * $$\sqrt{x^2+y^2} < r(h-z) \quad\text{and}\quad z>0.$$