The volumes of geometric shapes can be calculated from key measurements. This can be used to determine the size of a variety of lesions such as tumors or infarcts.

Shape |
Formula |
Variables |

cube |
a^3 |
a = length of side |

box |
a * b * c |
a, b, c = lengths of sides |

cylinder |
π * (R^2) * h |
R = radius of base h = height |

cone |
1/3 * π * (R^2) * h |
R = radius of base h = height |

truncated cone (frustrum) |
1/3 * π *h *((R1^2) + (R2^2) + (R1*R2)) |
R1 = radius of base R2 = radius at top h = distance between planes |

pyramid with square base |
1/3 * (a^2) * h |
a = length of base h = height |

truncated pyramid with square base (frustrum) |
1/3 * h * ((a^2) + (b^2) + (a * b)) |
a = side at base b = side at top h = distance between planes |

sphere |
4/3 * π * (R^3) |
R = radius |

zone and segment of sphere with 1 base |
1/6 * π * ((3* (r^2)) + (h^2)) |
r = radius at base h = distance to top |

zone and segment of sphere with 2 bases |
1/6 * π * h * ((3* (r1^2)) + (3* (r2^2)) + (h^2)) |
r1 = radius at base r2 = radius at top h = distance between planes |

ellipsoid |
4/3 * π * a * b * c |
a, b, c = lengths of semiaxes |

torus |
2 * π * R * (r^2) |
R = radius from center of space enclosed by inner ring to center of cross-section; r = radius of cross-section |

where:

• The length of a semiaxis for an ellipsoid is half of the measurement along the axis. If the entire axial measurement is used, then the volume = 1/6 * π * a * b * c