Density, Mass and Volume

Use density = mass ÷ volume.

So $80\text{ g}÷20{\text{ cm}}^3=4{\text{ g/cm}}^3$.

The density is 4 g/cm³.

Use mass = density × volume.

So $2.5{\text{ g/cm}}^3\times 8{\text{ cm}}^3=20\text{ g}$.

The mass is 20 g.

Use volume = mass ÷ density.

So $54\text{ g}÷2.7{\text{ g/cm}}^3=20{\text{ cm}}^3$.

The volume is 20 cm³.

Use density = mass ÷ volume.

So $15\text{ g}÷24{\text{ cm}}^3=0.625{\text{ g/cm}}^3$.

The density is 0.625 g/cm³.

(A common slip is to divide the wrong way round, $24÷15=1.6$. Mass always goes on top.)

First find the volume using volume = mass ÷ density. So $216\text{ g}÷8{\text{ g/cm}}^3=27{\text{ cm}}^3$.

For a cube, volume = side × side × side, so the side length is the cube root of the volume: $\sqrt[3]{27{\text{ cm}}^3}=3\text{ cm}$.

The side length is 3 cm.

(A common mistake is to stop at the volume, 27 cm³, and forget to take the cube root to get the side.)

We aren't given the volume, so find it first.

For a cuboid, volume = length × width × height $=6\text{ cm}\times 5\text{ cm}\times 2\text{ cm}=60{\text{ cm}}^3$.

Then use mass = density × volume. So $7.8{\text{ g/cm}}^3\times 60{\text{ cm}}^3=468\text{ g}$.

The mass is 468 g.