Formula Archimedes principle Buoyant Force Density Volume Gravitational acceleration
$$F_{\text A} ~=~ \class{blue}{\rho} \, \class{red}{V} \, g$$ $$F_{\text A} ~=~ \class{blue}{\rho} \, \class{red}{V} \, g$$ $$\class{blue}{\rho} ~=~ \frac{ F_{\text A} }{ g \, \class{red}{V} }$$ $$\class{red}{V} ~=~ \frac{ F_{\text A} }{ g \, \class{blue}{\rho} }$$ $$g ~=~ \frac{ F_{\text A} }{ \class{blue}{\rho} \, \class{red}{V} }$$
Buoyant Force
$$ F_{\text A} $$ Unit $$ \mathrm{N} $$ Force experienced by a body in the opposite direction to gravity when this body is immersed in a liquid (e.g. water). The body experiences a buoyancy.
Density
$$ \class{blue}{\rho} $$ Unit $$ \frac{ \mathrm{kg} }{ \mathrm{m}^3} $$ Mass density of the liquid. It tells you how heavy one cubic meter of the liquid is.
For example, the density of water is: \( \rho ~=~ 10^{-3} \, \frac{ \text{kg} }{ \text{m}^3} \).
Volume
$$ \class{red}{V} $$ Unit $$ \mathrm{m}^3 $$ Volume of the liquid displaced by the immersed body. This is exactly the volume of the body immersed in the liquid.
Gravitational acceleration
$$ g $$ Unit $$ \frac{\mathrm{m}}{\mathrm{s}^2} $$ The gravitational acceleration is experienced by a body in the gravitational field of a planet. On the earth the gravitational acceleration is: \( g ~=~ 9.8 \, \frac{\text m}{\text{s}^2} \).