# Sphere

- Sphere (a three-dimensional figure) has all points equally spaces from a given point of a three dimensional solid.
- Lune of a sphere is the space occupied by a wedge from the center of the sphere to the surface of the sphere.
- Sector of a sphere is the space occupied by a portion of the sphere with the vertex at the center and conical boundary.
- Segment and zone of a sphere is the space occupied by a portion of the sphere cut by two parallel planes.
- Sperical cap is the space occupied by a portion of the sphere cut by a plane.
- See Moment of Inertia of a Sphere

## Circumference of a Sphere formulas

\(\large{ C= 2 \; \pi \; r }\) | |

\(\large{ C= \pi \; d }\) |

### Where:

\(\large{ C }\) = circumference

\(\large{ d }\) = diameter

\(\large{ r }\) = radius

\(\large{ \pi }\) = Pi

## Diameter of a Sphere formula

\(\large{ d = 2\;r }\) |

### Where:

\(\large{ d }\) = diameter

\(\large{ r }\) = radius

## Luna of a Sphere formulas

\(\large{ S = 2\;r^2 \;theta }\) | |

\(\large{ S = \frac{\pi}{90} \;r^2 \;alpha }\) | |

\(\large{ V = \frac{2}{3} \;r^3 \;theta }\) | |

\(\large{ V = \frac{\pi}{270} \;r^3 \;alpha }\) |

### Where:

\(\large{ S }\) = surface area

\(\large{ V }\) = volume

\(\large{ \pi }\) = Pi

\(\large{ r }\) = radius

## Sector of a sphere formulas

\(\large{ S = 2\; \pi \;r \;h }\) | |

\(\large{ S = \pi \;r\; \left( 2\;h+r \right) }\) | |

\(\large{ V = \frac {2}{3}\; \pi \; r^2\;h }\) | |

\(\large{ V = \frac {2\; \pi \; r^2\;h}{3} }\) |

### Where:

\(\large{ S }\) = surface area

\(\large{ V }\) = volume

\(\large{ h }\) = height

\(\large{ \pi }\) = Pi

\(\large{ r }\) = radius

\(\large{ r_1 }\) = radius

## Segment and Zone of a Sphere formulas

\(\large{ S = 2\; \pi \;r \;h }\) | |

\(\large{ V = \frac{\pi}{6} \; \left(3\;r_1^2+ 3\;r_2^2+h^2\right)\;h }\) |

### Where:

\(\large{ S }\) = surface area

\(\large{ V }\) = volume

\(\large{ h }\) = height

\(\large{ \pi }\) = Pi

\(\large{ r_1 }\) = radius

\(\large{ r_2 }\) = radius of the top

## Spherical Cap formulas

\(\large{ r = \frac{h^2\;+\;r_2^2}{2\;h} }\) | |

\(\large{ S = 2\; \pi \;r \;h }\) |

### Where:

\(\large{ S }\) = surface area

\(\large{ h }\) = height

\(\large{ \pi }\) = Pi

\(\large{ r }\) = radius

## Surface Area of a sphere formula

\(\large{ S = 2\; \pi \;r^2 }\) |

### Where:

\(\large{ S }\) = surface area

\(\large{ \pi }\) = Pi

\(\large{ r }\) = radius

## Volume of a sphere formula

\(\large{ V = \frac{4}{3} \; \pi \;r^3 }\) |

### Where:

\(\large{ V }\) = volume

\(\large{ \pi }\) = Pi

\(\large{ r }\) = radius

Tags: Equations for Volume