Surface area is the Area of a given surface. Roughly speaking, it is the ``amount'' of a surface, and has units of distance squares. It is commonly denoted for a surface in 3-D, or for a region of the plane (in which case it is simply called ``the'' Area).

If the surface is Parameterized using and , then

(1) |

The surface area given by rotating the curve from to about the -axis is

(2) |

(3) |

The following tables gives surface areas for some common Surfaces. In the first table, denotes the lateral surface, and in the second, denotes the total surface. In both tables, denotes the Radius, the height, the base Perimeter, and the Slant Height (Beyer 1987).

Surface | |

Cone | |

Conical Frustum | |

Cube | |

Cylinder | |

Lune (Solid) | |

Oblate Spheroid | |

Prolate Spheroid | |

Pyramid | |

Pyramidal Frustum | |

Sphere | |

Torus | |

Zone |

Even simple surfaces can display surprisingly counterintuitive properties. For instance, the surface of revolution of
around the *x*-Axis for is called Gabriel's Horn, and has Finite Volume but
Infinite surface Area.

**References**

Beyer, W. H. *CRC Standard Mathematical Tables, 28th ed.* Boca Raton, FL: CRC Press, pp. 127-132, 1987.

© 1996-9

1999-05-26