how many plane surfaces does a cylinder have
two parallel planes two
title: Cylinder text: what we have called a cylindrical surface. To repeat, throughout this section a cylinder is defined as a surface consisting of all the points on all the lines which are parallel to a given line and which pass through a fixed plane curve in a plane not parallel to the given line. Such cylinders have, at times, been referred to as "". Through each point of a generalized cylinder there passes a unique line that is contained in the cylinder. Thus, this definition may be rephrased to say that a cylinder is any ruled surface spanned by a one-parameter family title: Cylinder text: hoped that context makes the meaning clear. In this article both points of view are presented and distinguished by referring to "solid cylinders" and "cylindrical surfaces", but keep in mind that in the literature the unadorned term cylinder could refer to either of these or to an even more specialized object, the "right circular cylinder". The definitions and results in this section are taken from the 1913 text, "Plane and Solid Geometry" by George Wentworth and David Eugene Smith . A "" is a surface consisting of all the points on all the lines which are parallel to a given title: Cylinder text: of solids of revolution. A cylindric section is the intersection of a cylinder's surface with a plane. They are, in general, curves and are special types of "plane sections". The cylindric section by a plane that contains two elements of a cylinder is a parallelogram. Such a cylindric section of a right cylinder is a rectangle. A cylindric section in which the intersecting plane intersects and is perpendicular to all the elements of the cylinder is called a "". If a right section of a cylinder is a circle then the cylinder is a circular cylinder. In more generality, if title: Constant-mean-curvature surface text: Constant-mean-curvature surface In differential geometry, constant-mean-curvature (CMC) surfaces are surfaces with constant mean curvature. This includes minimal surfaces as a subset, but typically they are treated as special case. Note that these surfaces are generally different from constant Gaussian curvature surfaces, with the important exception of the sphere. In 1841 Delaunay proved that the only surfaces of revolution with constant mean curvature were the surfaces obtained by rotating the roulettes of the conics. These are the plane, cylinder, sphere, the catenoid, the unduloid and nodoid. In 1853 J. H. Jellet showed that if formula_1 is a compact star-shaped surface in title: Cylinder text: parallel planes is called a (solid) '. The line segments determined by an element of the cylindrical surface between the two parallel planes is called an "element of the cylinder". All the elements of a cylinder have equal lengths. The region bounded by the cylindrical surface in either of the parallel planes is called a ' of the cylinder. The two bases of a cylinder are congruent figures. If the elements of the cylinder are perpendicular to the planes containing the bases, the cylinder is a ', otherwise it is called an '. If the bases are disks (regions whose