Question

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?

Answer 1

The density of the metal is `"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

`color(blue)(|bar(ul(color(white)(a/a) V = l^3color(white)(a/a)|)))" "`

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`