A right circular cylinder

An elliptic cylinder

In mathematics, a cylinder is a quadric surface, with the following equation in Cartesian coordinates:

This equation is for an elliptic cylinder, a generalization of the ordinary, circular cylinder (a = b). Even more general is the generalized cylinder: the cross-section can be any curve.

The cylinder is a degenerate quadric because at least one of the coordinates (in this case z) does not appear in the equation. By some definitions the cylinder is not considered to be a quadric at all.

In common usage, a cylinder is taken to mean a finite section of a right circular cylinder with its ends closed to form two circular surfaces, as in the figure (right). If the cylinder has a radius r and length (height) h, then its volume is given by

and its surface area is:

• Area of the top is πr²
• Area of the bottom is πr²
• Area of the side is 2πrh

Therefore without the top or bottom, the surface area is

A = 2πrh

With the top and bottom, the surface area is

For a given volume, the cylinder with the smallest surface area has h = 2r. For a given surface area, the cylinder with the largest volume has h = 2r, i.e. the cylinder fits in a cube (height = diameter.)

There are other more unusual types of cylinders. These are the imaginary elliptic cylinders:

the hyperbolic cylinder:

and the parabolic cylinder:

See also

• Steinmetz solid, the intersection of two or three perpendicular cylinders
• Prism (geometry)

Articles like Different types of cylinder e.g. circular cylinder, intersection of cylinders especially like circular cylinder with strait cylinder to be added here!

External links

• Surface Area MATHguide
• Volume MATHguide
• Spinning Cylinder Math Is Fun
• calculate surface area and volume with your own values
• Paper model cylinder

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Cylinder (geometry)

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