Discover

In mathematics, a 'cylinder' is a quadric surface, with the following equation in Cartesian coordinates:
:
ight)^2 + left(rac{y}{b}
ight)^2 = 1.
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
:$V\; =\; pi\; r^2\; h\; ,$
and its surface area is
:$A\; =\; 2\; pi\; r^2\; +\; 2\; pi\; r\; h\; =\; 2\; pi\; r\; (\; r\; +\; h\; ).,$
For a given volume, the cylinder with the smallest surface area has ''h'' = 2''r''. For a given surface area, the cylinder with the largest volume has ''h'' = 2''r'', i.e. the cylinder fits in a cube (height = diameter.)
There are other more unusual types of cylinders. These are the ''imaginary elliptic cylinders'':
:
ight)^2 + left(rac{y}{b}
ight)^2 = -1
the ''hyperbolic cylinder'':
:
ight)^2 - left(rac{y}{b}
ight)^2 = 1
and the ''parabolic cylinder'':
:$x^2\; +\; 2ay\; =\; 0.\; ,$

Contents

See also

External links

See also

★ Steinmetz solid, the intersection of two or three perpendicular cylinders

★ Prism (geometry)

External links

★ Surface Area MATHguide

★ Volume MATHguide

★ Spinning Cylinder Math Is Fun

★ calculate surface area and volume with your own values

★ Paper model cylinder