# Density: Formula and units

## In a nutshell

Density is a measure of how heavy $1cm^3$ of a material is. Another way of saying this is that density is *the mass per unit volume* of a material. Every material has its own density.

## Density formula

The density of a material is given as:

$density=\frac{mass}{volume}$

Or, more simply:

$D=\frac{M}{V}$

## Units of density, mass and volume

#### Measurement | #### Units |

Density | kilograms per cubic metre ($kg/m^3$), grams per cubic centimetre ($g/cm^3$) |

Mass | kilograms ($kg$), grams ($g$) |

Volume | cubic metres ($m^3$), cubic centimetres ($cm^3$) |

## Solving density problems

To solve problems involving density, follow this procedure:

#### procedure

1. | Identify what values you have and what variable you want to find. |

2. | Rearrange the density formula for the desired variable. |

3. | Substitute in known values. |

4. | Give the answer with the correct units. |

##### Example 1

*The density of gold is $19{,}300kg/m^3$. A bar of gold weighs $4{,}000kg$. What is the volume of this bar to two decimal places?*

*From the given information, identify the density and the mass:*

$D=19{,}300kg/m^3,\,M=4{,}000kg$

*Write down the density formula:*

$D=\frac{M}{V}$

*Rearrange the density formula for volume:*

$V=\frac{M}{D}$

*Substitute in the known values:*

$V=\frac{4000kg}{19300kg/m^3}$

*Give the answer with the correct units:*

$V=0.207253886...m^3$

*Round to two decimal places, like the question asks:*

$\underline{V=0.21m^3}$__,__ to two decimal places.