# The density of a sample of aluminum is 2.70 g/cm3. You submerse a sample of aluminum in water, and the volume of the water rises 1.3 L (1.3 L is displaced by the aluminum). Using the correct number of significant figures, what is the mass of the sample?

Oct 16, 2016

The mass of aluminum is 3500 g, rounded to two significant figures.

#### Explanation:

Density is mass per unit of volume.

$\text{density"="mass"/"volume}$

The displaced volume of water is the volume of the aluminum sample.

Since the given density is in ${\text{g/cm}}^{3}$, the unit for the volume of water needs to be converted to ${\text{cm}}^{3}$.

$\text{1 L=1000 mL}$
$\text{1 mL=1 cm"^3}$

$1.3 \cancel{\text{L"xx(1000cancel"mL")/(1cancel"L")xx(1"cm"^3)/(1cancel"mL")="1300 cm"^3}}$

In order to determine the mass of an object when its density and volume are known, the equation needs to be rearranged to isolate $\text{mass}$

$\text{mass"="density"xx"volume}$

Substitute the given density and volume into the equation and solve.

$\text{mass"=2.70"g"/cancel"cm"^3xx1300cancel"cm"^3"=3510 g"=3500 "g}$ rounded to two significant figures