# A small cube of metal measures 19.4 mm on a side and weighs 80.1 g. What is the density of the metal in g/cm^3?

Sep 5, 2016

The density of the metal is ${\text{11.0 g/cm}}^{3}$.

#### Explanation:

The density(ρ) of anything is its mass ($m$) divided by its volume ($V$).

color(blue)(|bar(ul(color(white)(a/a) ρ = m/Vcolor(white)(a/a)|)))" "

The volume of a cube is

$\textcolor{b l u e}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} V = {l}^{3} \textcolor{w h i t e}{\frac{a}{a}} |}}} \text{ }$

where $l$ is the length of an edge.

V = l^3 = ("19.4 mm")^3 = "7301 mm"^3

We must convert cubic millimetres to cubic centimetres.

V = 7301 color(red)(cancel(color(black)("mm"^3))) × ("1 cm"/(10color(red)(cancel(color(black)("mm")))))^3 = "7.301 cm"^3

ρ = m/V = "80.1 g"/("7.301 cm"^3) = "11.0 g/cm"^3