In mathematics a cylinder is a quadric, i.e. a three-dimensional surface, with the following equation in Cartesian coordinates:
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 h, then its volume is given by
There are other more unusual types of cylinder. These are the imaginary elliptic cylinder:
A cylinder in an engine is the space a piston travels in. The piston is the same size as the two bases of the cylinder (the circular and flat surfaces). In the following drawing, which depicts a cross-section of a steam engine cylinder, the bottom sliding part is the piston, and the top sliding part is a valve that directs steam into the two ends of the cylinder alternately.
The cylinder was also the dominant medium of audio storage from the 1870s to the 1910s, and continued in limited use (such as the dictaphone) through the mid 20th century. See: phonograph cylinder.