Question

Question #337cb

Answer 1

`"55 cm"^3`

Explanation:

The thing to remember about the density of a given substance is that it tells you the mass of exactly `1` unit of volume of that substance.

In your case, you know that the density of steel is equal to `"7.8 g cm"^(-3)`. This value tells you that every `"1 cm"^3` of steel, the equivalent of one unit of volume, has a mass of `"7.8 g"`.

So if you know that you need `"7.8 g"` of steel in order to have `"1 cm"^3` of steel, you can say that `"430 g"` of steel would correspond to a volume of

`430 color(red)(cancel(color(black)("g"))) * "1 cm"^3/(7.8color(red)(cancel(color(black)("g")))) = color(darkgreen)(ul(color(black)("55 cm"^3)))`

The answer is rounded to two sig figs.

So remember, every time you have the density of a substance, you can use it as a conversion factor to find the mass of a given volume or the volume of a given mass.

For this example, you would have

`"mass " -> " volume:" " " "1 cm"^3/"7.8 g"`

`"volume " -> " mass:" " " "7.8 g"/"1 cm"^3`