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?

1 Answer
Simon Moore · Stefan V.
Mar 4, 2016

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

Explanation:

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"#

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