Surface of revolution

A surface formed by rotating a curve around an axis in three-dimensional space. Its shape depends on the generating curve and its position relative to the axis.

Axis of revolution: A fixed line about which a curve or another geometric object is rotated. Its position determines the orientation and shape of the resulting surface.
Curve: A continuous geometric object that may be described by equations or parameterized by one variable. The curve supplies the profile that rotation sweeps into a surface.
Sphere: The three-dimensional set of points at a fixed distance from a center. Rotating a semicircle around its diameter generates a sphere.
Surface area of revolution: The area of a surface generated by rotating a curve around an axis. Rotating an arc-length element determines the surface-area integral.
Ruled surface: A surface that can be swept out by a moving straight line. A surface of revolution need not be ruled, though cylinders and cones are.
Parametric surface: A surface described by a map from two parameters to points in three-dimensional space. A rotating curve can be parameterized by its curve position and rotation angle.
Cartesian coordinate system: A coordinate system that locates points using signed distances along perpendicular axes. Coordinates make the rotation axis and generating curve precise.
Cylinder: A solid with two parallel congruent bases joined by a curved lateral surface. Rotating a line segment parallel to the axis produces a cylindrical surface.
Volume of revolution: The volume of a solid formed by rotating a plane region around an axis. The same rotation can sweep a solid whose volume is computed by disks or shells.
Translational surface: A surface generated by translating one curve along another curve. Translation generates surfaces without the circular symmetry characteristic of revolution.

Linked from 5 pages