# A piece of metal weighs 3.94 g and has a density of 5.674 g/cm^3. What's the volume?

Jan 2, 2016

The volume is $\text{0.694 cm"^3}$.

#### Explanation:

The formula for density is $\text{D"="M"/"V}$, where $\text{D}$ is density, $\text{M}$ is mass, and $\text{V}$ is volume.

Given
$\text{D=5.674 g/cm"^3}$
$\text{M=3.94 g}$

Unknown
$\text{V}$

Solution
Rearrange the equation to isolate $\text{V}$, substitute the given values into the equation and solve.

$\text{D"="M"/"V}$

$\text{V"="M"/"D}$

Remember when you divide by a fraction like $\text{g"/"cm"^3}$, you multiply times its multiplicative inverse, $\text{cm"^3/"g}$.

$\text{V"=3.94cancel"g"xx(1"cm"^3)/(5.674cancel"g")="0.694 cm"^3}$

The Density Pyramid below can help you remember how to solve density problems. Cover the variable for which you need to solve. The placement of the known variables on the pyramid will indicate how to solve. For example, if you need density, cover D. M is over V, so you divide Mass by Volume.

If you need volume, cover V. M is over D, so you divide Mass by Density.

If you need mass, cover M. D is next to V, so multiply Density times Volume.