# Question #337cb

Feb 24, 2018

${\text{55 cm}}^{3}$

#### 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 ${\text{7.8 g cm}}^{- 3}$. This value tells you that every ${\text{1 cm}}^{3}$ of steel, the equivalent of one unit of volume, has a mass of $\text{7.8 g}$.

So if you know that you need $\text{7.8 g}$ of steel in order to have ${\text{1 cm}}^{3}$ of steel, you can say that $\text{430 g}$ of steel would correspond to a volume of

$430 \textcolor{red}{\cancel{\textcolor{b l a c k}{{\text{g"))) * "1 cm"^3/(7.8color(red)(cancel(color(black)("g")))) = color(darkgreen)(ul(color(black)("55 cm}}^{3}}}}$

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

$\text{mass " -> " volume:" " " "1 cm"^3/"7.8 g}$

${\text{volume " -> " mass:" " " "7.8 g"/"1 cm}}^{3}$