Cone, in geometry, a solid figure described by a straight line moving in such a way that it always passes through a given curve enclosing a portion of a plane and through a fixed point not in that plane. The fixed point is called the vertex of the cone, and the portion of the plane enclosed by the given curve is called the base of the cone. When the base is a circle, and the line drawn from the vertex to the centre of the circle is perpendicular to the plane of the circle, the figure is called a right cone. If the line drawn from the vertex to the centre of the base is not perpendicular to the plane of the base, the figure is called an oblique cone. So if a right-angled triangle be revolved about one of the sides forming the right angle, the other side will describe a circle and the hypothenuse will describe a right cone. In popular usage the cone is considered as limited to that portion of the figure between the vertex and the base; but in mathematics the line describing the cone is supposed to extend indefinitely beyond the base, and the mathematical cone is consequently a figure of boundless extent. Every straight line drawn from the vertex through the curve enclosing the base is called a side of the cone.

Every such line of course represents one of the positions of the line by which the cone is supposed to have been described. The distance from the vertex to the base measured on any one of these lines is called the slant height. The perpendicular distance from the vertex to the plane of the base is called the altitude of the cone. The study of the right cone is sufficient for most practical and scientific purposes. (See Conic Sections.) The area of the surface of a right cone is equal to one half the circumference of the base multiplied by the slant height. The volume or solidity of a right cone is equal to one third the area of the base multiplied by the altitude. - The name cone is given to the fruit of the pines and larches, from their resemblance to this figure.