In common usage and elementary geometry, a **cone** 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 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**).

## 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* = π*r*^{2}*h* / 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.

The surface area *A* is given by *A* = π*r*(*r* + *s*), where is the "slant height" of the cone. The first term in the area formula, π*r*^{2}, is the area of the base; while the second term, π*r**s*, is the area of the curved side surface.

## See also

Last updated: 02-10-2005 21:08:10

Last updated: 05-03-2005 09:00:33