A spherical cap is the region of a Sphere which lies above (or below) a given Plane. If the Plane passes
through the Center of the Sphere, the cap is a Hemisphere. Let the Sphere have Radius ,
then the Volume of a spherical cap of height and base Radius is given by the equation of a
Spherical Segment (which is a spherical cut by a second Plane)

(1) |

(2) |

(3) |

(4) |

(5) |

(6) |

(7) |

(8) |

Consider a cylindrical box enclosing the cap so that the top of the box is tangent to the top of the Sphere. Then the
enclosing box has Volume

(9) |

so the hollow volume between the cap and box is given by

(10) |

If a second Plane cuts the cap, the resulting Spherical Frustum is called a Spherical Segment.
The Surface Area of the spherical cap is given by the same equation as for a general Zone:

(11) |

© 1996-9

1999-05-26