Question

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?

Answer 1

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

Explanation:

Density is mass per unit of volume.

`"density"="mass"/"volume"`

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

Since the given density is in `"g/cm"^3`, the unit for the volume of water needs to be converted to `"cm"^3`.

`"1 L=1000 mL"`
`"1 mL=1 cm"^3"`

`1.3cancel"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 `"mass"`

`"mass"="density"xx"volume"`

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

`"mass"=2.70"g"/cancel"cm"^3xx1300cancel"cm"^3"=3510 g"=3500 "g"` rounded to two significant figures