# A sample of steel with a density of 7.81 g/ml is added to a 100-mL graduated cylinder with 45.0mL of water. If the resulting water level is 55.5 mL, what is the mass of the sample of steel?

Mar 4, 2016

Just over $\text{82 g}$ ($\text{82.005 g}$, if you assume a water density of $\text{1.00 g/ml}$).

#### Explanation:

The water level rose from $\text{45 ml}$ to $\text{55.5 ml}$, so that is a volume increase of $\text{10.5 ml}$.

Assuming that the density of the water is $\text{1.00 g/ml}$, then we know that the volume of the steel sample was $\text{10.5 ml}$, and we know it has a density of $\text{7.81 g/ml}$.

So now we can work out the mass. We know that

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

therefore

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

Therefore the mass is

$10.5 \times 7.81 = \text{82.005 g}$