# Question e7f3f

May 25, 2015

The volume of the container will be ${\text{66 cm}}^{3}$.

For any given substance, density is defined as mass per unit of volume.

$\rho = \frac{m}{V}$

In your case, a density of ${\text{12.2 g/cm}}^{3}$ means that each ${\text{cm}}^{3}$ of your substance has a mass of 12.2 g.

This is equivalent to saying that 12.2 g of your substance will occupy exactly ${\text{1 cm}}^{3}$. Since you're dealing with more than 12.2 g, the volume of your sample will of course be bigger than ${\text{1 cm}}^{3}$.

Notice that the mass of the substance is given in kilograms. This means that you have to convert it into grams in order to get to match the units given for density.

0.8cancel("kg") * "1000 g"/(1cancel("kg")) = "800 g"

This means that the volume of the sample will be

800cancel("g") * ("1 cm"^3)/(12.2cancel("g")) = "65.57 cm"^3#

Now, since you only gave one sig fig for the mass of the substance, the answer *should be * given as

$V = {\text{70 cm}}^{3}$

However, I'll leave the answer with 2 sig figs because I suspect the mass of the substance was actually 0.80 kg

$V = {\text{66 cm}}^{3}$

You can use whichever value fits your actual data.