# conical surface

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## cone

, in mathematics

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 and the area of the base. The frustum of a cone is the portion of the cone between the base and a plane parallel to the base of the cone cutting the cone in two parts.

## conical surface

[′kän·ə·kəl ′sər·fəs]
(mathematics)
A surface formed by the lines which pass through each of the points of a closed plane curve and a fixed point which is not in the plane of the curve.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.

## conical surface

A surface extending from the periphery of the horizontal surface outward and upward at a slope of 20 horizontal to 1 vertical for a horizontal distance of 4000 ft. It is an imaginary surface, in which any object that projects above the surface is considered an obstruction to air navigation.