 x Cone (geometry) Overview

A cone is an -dimensional
Dimension
In physics and mathematics, the dimension of a space or object is informally defined as the minimum number of coordinates needed to specify any point within it. Thus a line has a dimension of one because only one coordinate is needed to specify a point on it...

geometric shape that tapers smoothly from a base (usually flat and circular) to a point called the apex or vertex. Formally, it is the solid figure formed by the locus
Locus (mathematics)
In geometry, a locus is a collection of points which share a property. For example a circle may be defined as the locus of points in a plane at a fixed distance from a given point....

of all straight line segments that join the apex to the base. The term "cone" is sometimes used to refer to the surface or the lateral surface of this solid figure (the lateral surface of a cone is equal to the surface minus the base).

The axis of a cone is the straight line (if any), passing through the apex, about which the base has a rotational symmetry
Rotational symmetry
Generally speaking, an object with rotational symmetry is an object that looks the same after a certain amount of rotation. An object may have more than one rotational symmetry; for instance, if reflections or turning it over are not counted, the triskelion appearing on the Isle of Man's flag has...

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In common usage in elementary geometry
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....

, cones are assumed to be right circular, where right means that the axis passes through the centre of the base (suitably defined) at right angles
Perpendicular
In geometry, two lines or planes are considered perpendicular to each other if they form congruent adjacent angles . The term may be used as a noun or adjective...

to its plane, and circular means that the base is a circle
Circle
A circle is a simple shape of Euclidean geometry consisting of those points in a plane that are a given distance from a given point, the centre. The distance between any of the points and the centre is called the radius....

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