# Volume

Volume, abbreviated as V, is the space occupied by a mass. Volume is a extensive variable whose values depend on the quantity of substance under study. It is expressed in terms of length cubed, a quantity of three dimensional space occupied by gas, liquid, or solid. Volume is a scalar quantity having direction, some of these include area, density, energy, entropy, length, mass, power, pressure, speed, temperature, and work.

## Volume formula

\(\large{ V = l \; w \; h }\) |

### Where:

Units |
English |
Metric |

\(\large{ V }\) = volume | \(\large{ft^3}\) | \(\large{m^3}\) |

\(\large{ h }\) = height | \(\large{ft}\) | \(\large{m}\) |

\(\large{ l } \) = length | \(\large{ft}\) | \(\large{m}\) |

\(\large{ w }\) = width | \(\large{ft}\) | \(\large{m}\) |

## Related formulas

\(\large{ V = \frac{ m }{ \rho } }\) | (Density) (Mass) |

\(\large{ V = a^3 }\) | (Cube) |

\(\large{ V= \frac{1}{2} \; \pi \; a^2 \;h }\) | (Elliptic Paraboloid) |

\(\large{ V = \frac {n \; R \; T}{p} }\) | (Ideal Gas Law) |

\(\large{ V = \frac{l\;b\;h}{2} }\) | (Isosceles Triangle Wedge) |

\(\large{ V = \pi\; r^2\;h }\) | (Oblique Cylinder) |

\(\large{ V = \frac {1}{3}\; \pi\; r^2 }\) | (Right Cone) |

\(\large{ V = \pi\; r^2\;h }\) | (Right Cylinder) |

\(\large{ V = \pi\; a_a \;b_a\; h }\) | (Right Elliptic Cylinder) |

\(\large{ V = \frac {3\; \sqrt {3} } { 2 } \; a^2\;h }\) | (Right Hexagon Prism) |

\(\large{ V = \pi\; r_i^2\;h }\) | (Right Hollow Cylinder (Inside) ) |

\(\large{ V = \pi\; h \left(R_o^2 - r_i^2 \right) }\) | (Right Hollow Cylinder (Object) ) |

\(\large{ V= \frac {1}{4} \; \sqrt { 5\; \left ( 5+2\; \sqrt {5} \right) } \;a^2\;h }\) | (Right Pentagonal Prism) |

\(\large{ V= \frac{5}{6}\; r\;a\;h }\) | (Right Pentagonal Pyramid) |

\(\large{ V= a\;b\;h }\) | (Right Rectangular Prism) |

\(\large{ V=a^2\;h }\) | (Right Square Prism) |

\(\large{ V= a^2\; \frac{h}{3} }\) | (Right Square Pyramid) |

\(\large{ V=\frac{1}{6}\; h_b\;a\;h }\) | (Right Triangular Prism) |

\(\large{ V = \frac{l\;a\;b}{2} }\) | (Right Triangle Wedge) |

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

\(\large{ V = 2 \; \pi^2 \; R_s\; r_s^2 }\) | (Torus) |

### Where:

\(\large{ V }\) = volume

\(\large{ A_b }\) = base area

\(\large{ \rho }\) (Greek symbol rho) = density

\(\large{ a, b, c }\) = edge

\(\large{ h }\) = height

\(\large{ h_b }\) = height base

\(\large{ l } \) = length

\(\large{ a_a }\) = length semi-major axis

\(\large{ b_a }\) = length semi-minor axis

\(\large{ n }\) = number of moles of gas

\(\large{ m }\) = mass

\(\large{ n }\) = mole

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

\(\large{ p }\) = pressure

\(\large{ r }\) = radius

\(\large{ r_s }\) = radius of sphere

\(\large{ R_s }\) = radius of center of sphere

\(\large{ r_i }\) = inside radius

\(\large{ R_o }\) = outside radius

\(\large{ p_s }\) = shape parameter

\(\large{ R }\) = specific gas constant (gas constant)

\(\large{ tan }\) = tangent

\(\large{ T }\) = temperature