 In common usage and elementary geometry, a cone (Greek: κώνος) is a solid object obtained by rotating a right triangle around one of its two short sides, the cone's axis. The disk swept by the other short side is called the base, and the endpoint of the axis which is not on the base is the cone's apex or vertex. An object shaped like a cone is said to be conical. A cone. ...
Geometry (Greek γεωμετÏία; geo = earth, metria = measure) arose as the field of knowledge dealing with spatial relationships. ...
For alternate meanings, such as the musical instrument, see triangle (disambiguation). ...
The axis of rotation of a rotating body is a line such that the distance between any point on the line and any point of the body remains constant under the rotation. ...
A synonym for ball (in geometry or topology, and in any dimension) is disk (or disc Geometry In metric geometry, a ball is a set containing all points within a specified distance of a given point. ...
A cone with its apex cut off by a plane parallel to its base is called a frustum. The term cone is sometimes extended to more general shapes, such as the image of a common cone by an affine map — which may turn the basis into an ellipse (producing an elliptical cone) and/or tilt the axis relative to the base (an oblique cone). (See conical surface and conic solid for further generalization.) This article is in need of attention from an expert on the subject. ...
A frustum is the portion of a solid – normally a cone or pyramid – which lies between two parallel planes cutting the solid. ...
In mathematics, a function is a relation, such that each element of a set (the domain) is associated with a unique type of another (possibly the same) set (the codomain, not to be confused with the range). ...
An affine transformation or affine map (from the Latin, affinis, connected with) between two vector spaces consists of a linear transformation followed by a translation. ...
In mathematics, an ellipse (from the Greek for absence) is a plane algebraic curve where the sum of the distances from any point on the curve to two fixed points is constant. ...
In geometry, a (general) conical surface is the unbounded surface formed by the union of all the straight lines that pass through a fixed point — the apex or vertex — and any point of some fixed space curve — the directrix — that does not contain the apex. ...
A conic solid is the locus of all line segments between a simply connected region of a plane (the base) and a point (the apex) outside the plane. ...
Formulas
The volume, V, of a cone of height, h, and base radius, r, is 1/3 of the volume of the cylinder with the same dimensions, i.e. V = πr2h / 3. The center of mass (assuming the cone is filled with uniform density) is located on the axis, 1/4 of the way from base to apex. Volume, also called capacity, is a quantification of how much space an object occupies. ...
A right circular cylinder In mathematics, a cylinder is a quadric, i. ...
The surface area A is given by A = πr(r + s), where  is the "slant height" of the cone. The first term in the area formula, πr2, is the area of the base; while the second term, πrs, is the area of the curved side surface. Area is a physical quantity expressing the size of a part of a surface. ...
Surface Area = Base Area + Lateral Area
See also A cone is a basic geometrical shape: see cone (solid). ...
In geometry, a (general) conical surface is the unbounded surface formed by the union of all the straight lines that pass through a fixed point — the apex or vertex — and any point of some fixed space curve — the directrix — that does not contain the apex. ...
In mathematics, a conic section (or just conic) is a curved locus of points, fby intersecting a cone with a plane. ...
A frustum is the portion of a solid – normally a cone or pyramid – which lies between two parallel planes cutting the solid. ...
For other versions including architectural Pyramids, see Pyramid (disambiguation). ...
Ellipsoid Elliptic Paraboloid Hyperbolic Paraboloid Hyperboloid of One Sheet Hyperboloid of Two Sheets Cone Elliptic Cylinder Hyperbolic Cylinder Parabolic Cylinder In mathematics a quadric, or quadric surface, is any D-dimensional (hyper-)surface represented by a second-order equation in spatial variables (coordinates). ...
In geometry, a surface is ruled if through every point of there is a straight line that lies on . ...
Hyperboloid of one sheet Hyperboloid of two sheets In mathematics, a hyperboloid is a quadric, a type of surface in three dimensions, described by the equation: (hyperboloid of one sheet), or (hyperboloid of two sheets) If, and only if, , it is a hyperboloid of revolution. ...
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