Volume

Written by Jerry Ratzlaff on . Posted in Solid Geometry

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 formulas

 $$\large{ V = l \; w \; h }$$ $$\large{ V = \frac{ m }{ \rho } }$$ (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

$$\large{ w }$$ = width