cone or conical surface, in mathematics, surface generated by a
moving line (the generator) that passes through a given fixed
point (the vertex) and continually intersects a given fixed
curve (the directrix). The generator creates two conical
surfaces—one above and one below the vertex—called nappes. If
the directing curve is a conic section (e.g., a circle or
ellipse) the cone is called a quadric cone. The most common type
of cone is the right circular cone, a quadric cone in which the
directrix is a circle and the line drawn from the vertex to the
center of the circle is perpendicular to the circle. The
generator of a cone in any of its positions is called an
element. The solid bounded by a conical surface and a plane (the
base) whose intersection with the conical surface is a closed
curve is also called a cone. The altitude of a cone is the
perpendicular distance from its vertex to its base. The lateral
area is the area of its conical surface. The volume is equal to
one third the product of the altitude an