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 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