Question

The density of gold is `19.3 g``/``cm^3`. What is the volume, in `cm^3`, of a sample of gold with mass `0.715` `kg`? If this sample of gold is a cube, how long is each edge in `cm`?

Answer 1

The volume is `"37.0 cm"^3 "Au"`.
Each side is `root(3)(37.0"cm"^3)~~"3.332 cm"^3"`

Explanation:

Given/Known

Density`=` `"19.3 g/cm"^3"`

Mass`=` `0.715cancel"kg"xx(1000"g")/(1cancel"kg")="715 g"`

Equation
`"density"=("mass")/("volume")`

Solution
Rearrange the equation to isolate volume and solve.
`"volume"=("mass")/("volume")`

`"volume"=(715cancel"g"Au")/(19.3 cancelg/(cm^3)` `=` `"37.0 cm"^3 "Au"`

Sides of the Cube

Since all sides of a cube are equal, the volume of a cube is `"s"^3"`, where `"s"` is one side. If you have the volume of the cube, you can take the cube root of the volume to find the value of each side of the cube.

Each side`=` `root(3)(37.0"cm"^3)~~"3.332 cm"`