Compound units and conversions

Objective. Convert area and volume units and solve measure problems.

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2. Worked example
3. Practice
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Learn: the key idea

Converting area and volume units requires squaring or cubing the linear conversion factor, since area scales with length squared and volume scales with length cubed. To convert cm² to m², divide by 100² = 10 000, and to convert cm³ to m³, divide by 100³ = 1 000 000. A floor area of 50 000 cm² converts to 50 000 ÷ 10 000 = 5 m², while a tank volume of 2 000 000 cm³ converts to 2 000 000 ÷ 1 000 000 = 2 m³. Always square or cube the linear factor rather than using it unchanged.

Worked example

Convert a volume of 3 500 000 cm³ into cubic metres using compound unit conversion.

1 $Recall the conversion factor: 1 m³ = 100³ cm³ = 1 000 000 cm³$
2 $Divide the volume by this factor: 3 500 000 \div 1 000 000$
3 $Calculate: 3 500 000 \div 1 000 000 = 3.5$
4 $The volume is 3.5 m³$

Answer: 3.5 m³

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Common mistake. Pupils often convert cm² to m² by dividing by 100 instead of 10 000, forgetting that area conversion needs the factor squared. Always square the linear conversion factor for area and cube it for volume.

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