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?

Just over ##"82 g"## (##"82.005 g"##, if you assume a water of ##"1.00 g/ml"##).

The water level rose from ##"45 ml"## to ##"55.5 ml"##, so that is a volume increase of ##"10.5 ml"##.

Assuming that the density of the water is ##"1.00 g/ml"##, then we know that the volume of the steel sample was ##"10.5 ml"##, and we know it has a density of ##"7.81 g/ml"##.

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

##"density" = "mass"/"volume"##

therefore

##"mass" = "volume" xx "density"##

Therefore the mass is

##10.5 xx 7.81 = "82.005 g"##