Density and pressure

Objective. Rearrange and use compound-measure formulae.

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Learn: the key idea

Density and pressure are compound measures built from two other quantities, where density = mass ÷ volume and pressure = force ÷ area. These formulae can be rearranged, so mass = density × volume, or force = pressure × area, depending on which quantity is unknown. For example, if a block has a mass of 50 g and a volume of 10 cm³, its density is 50 ÷ 10 = 5 g/cm³, and this rearranges to find volume as mass ÷ density if needed. Correct units must be carried through every calculation, since density is often measured in g/cm³ or kg/m³ and pressure in N/m² or pascals.

Worked example

A metal block has a mass of 270 g and a volume of 30 cm³. Calculate its density.

1 $The formula for density is mass \div volume.$
2 $Substitute the given values: 270 \div 30.$
3 $Carry out the division: 270 \div 30 = 9.$
4 $Attach the correct units for density, g/cm³.$

Answer: 9 g/cm³

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Common mistake. Pupils often divide volume by mass instead of mass by volume when finding density, inverting the formula and producing a value with the wrong units. Always check which quantity is being divided by which using the formula's definition.

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