Surfaces Of Revolution:

Surface of revolution is a method of producing a three-dimensional surface by revolving a two-dimensional entity, such like, a line, a plane curve, around an axis in space. For simplicity, at first the axis of rotation is supposed coincident with the x-axis and in the positive direction. The line, point or plane curve to be rotated is supposed to lie in the xy-plane.

The simplest entity as a point is rotated around an axis which does not lie on the axis is rotated around an angle of 2π yields a circle. Rotation through an angle less than 2π yields a circular arc.

If the entity is a line segment parallel to and not coincident along with the axis of rotation and rotation from an angle of 2π (360°) yields a circular cylinder. The radius of the cylinder is the perpendicular distance through the line to the rotation axis. The length of the cylinder is the length of the line segment.