Cylinder.

Cylinder. Cylinder, three-dimensional geometric figure. A circular cylinder consists of two circular bases of equal area that are in parallel planes, and are connected by a lateral surface that intersects the boundaries of the bases. The volume of a circular cylinder is pr2h, where r is the radius of the bases, and h is the perpendicular distance between the planes that contain the bases. In a right circular cylinder, the lateral surface is perpendicular to the bases. The lateral surface area of a right circular cylinder is 2prh,, and the total surface area is 2pr(r+h ). More generally, a cylinder need not have circular bases, nor must a cylinder form a closed surface. If MNPQ is a curve in a plane (Fig. 1), and APB is a line that is not in the plane and that intersects the curve at a point P, then all lines parallel to AB and intersecting MNQ when taken together form a cylindrical surface. If the curve MNPQ is closed, the volume enclosed is a cylindrical solid. The term cylinder may refer to either the solid or the surface. The line APB, or any other line of the surface that is parallel to APB, is called a generatrix or element of the cylinder, and the curve MNPQ is called a directrix or base. In a closed cylinder, all the elements taken together form the lateral surface. A closed cylinder is circular, elliptical, triangular, and so on, according to whether its directrix is a circle, ellipse, or triangle. In a right cylinder, all elements are perpendicular to the directrix; in an oblique cylinder, the elements are not perpendicular to the directrix. In general, the volume of a closed cylinder between the base and a plane parallel to it is given by Bh, in which B is the area of the base and h is the perpendicular distance between the two parallel planes; see Fig. 2. See Solid Geometry. Microsoft ® Encarta ® 2009. © 1993-2008 Microsoft Corporation. All rights reserved.