Chemistry / Unit 1 Chem 0107 worked example, 60 to 90 seconds
Calculating Density from Mass and Volume
The idea
Calculating density means measuring an object's mass and volume separately, by balance and by geometry or displacement, then dividing mass by volume, carrying the unit through the division.
In practice
A metal cube with an edge length of 2.00 cm has a volume of 2.00 × 2.00 × 2.00 = 8.00 cm³. If the cube's mass on a balance reads 90.7 g, its density is 90.7 g ÷ 8.00 cm³ ≈ 11.3 g/cm³, a figure that already reflects three significant figures. A liquid sample poured into a graduated cylinder shows a similar pattern: 45.0 mL of an unknown liquid with a mass of 35.6 g yields 35.6 g ÷ 45.0 mL ≈ 0.791 g/mL, a value low enough to suggest an alcohol rather than water.
Where people slip
Students sometimes invert the ratio, dividing volume by mass instead of mass by volume, which produces a reciprocal unit like cm³/g instead of g/cm³ — checking that the result's units read mass over volume catches the error immediately.
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