A
cylinder is one of the most basic curvilinear geometric shapes the
surface formed by the points at a fixed distance from a given
straight line, the
axis of the cylinder. The solid enclosed by this surface and by two planes perpendicular to the axis is also called a cylinder. The
surface area and the
volume of a cylinder have been known since deep antiquity.
In differential geometry, a cylinder is defined more broadly as any ruled surface spanned by a one-parameter family of parallel lines. The most common type of such generalized cylinders is given by certain quadric surfaces. A cylinder whose cross section is an ellipse, parabola, or hyperbola is called an elliptic cylinder, parabolic cylinder, or hyperbolic cylinder.
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
