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Metric Area and Volume Units

FoundationHigherAQAEdexcelOCR

Master metric area and volume units for GCSE Maths with structured, exam-style practice. This Foundation and Higher resource covers converting metric area and volume units and includes a complete mark scheme showing the steps examiners reward. Suitable for AQA, Edexcel and OCR. Free to download as a PDF. There are 100² cm² in 1 m² and 100³ cm³ in 1 m³.

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These worksheets and mark schemes are original, written for Virtus Academy and checked against the current AQA, Edexcel and OCR specifications. Every worksheet comes with a full mark scheme.

Foundation

WorksheetFoundation · PDFMark SchemeFoundation · PDF

Higher

WorksheetHigher · PDFMark SchemeHigher · PDF

Topic overview

Converting between units of area and volume is not the same as converting lengths, and this catches out a great many students.

Since \(1\)m is \(100\)cm, it might seem that \(1\)m² is \(100\)cm². It is not. A square metre is \(100\)cm by \(100\)cm, which is \(10\,000\)cm², so the length conversion factor is squared.

The same logic applies to volume, where the factor is cubed. One cubic metre is \(100 \times 100 \times 100 = 1\,000\,000\)cm³. Sketching the square or cube and labelling its sides makes the reason obvious and the factor easy to derive rather than memorise.

Revision notes

Area conversions

Square the length conversion factor.

Since \(1\)m \(= 100\)cm, \(1\)m² \(= 100^2 = 10\,000\)cm². Similarly \(1\)cm² \(= 10^2 = 100\)mm².

Volume conversions

Cube the length conversion factor.

Since \(1\)m \(= 100\)cm, \(1\)m³ \(= 100^3 = 1\,000\,000\)cm³. And \(1\)cm³ \(= 1000\)mm³.

Capacity

Capacity links to volume: \(1\)ml is exactly \(1\)cm³, and \(1\) litre is \(1000\)cm³.

This lets you move between volume and capacity directly, which many real-world questions require.

Key points

  • Area factors are the length factor squared.
  • Volume factors are the length factor cubed.
  • \(1\)m² \(= 10\,000\)cm².
  • \(1\)m³ \(= 1\,000\,000\)cm³.
  • \(1\)ml \(= 1\)cm³.
  • \(1\) litre \(= 1000\)cm³.

Worked examples

Example 1

Convert \(3\)m² to cm².

Working

\[1\text{m}^2 = 100^2 = 10\,000\text{cm}^2\]square the length conversion factor
\[3 \times 10\,000\]multiply by the number of square metres
\[= 30\,000\text{cm}^2\]state the answer

Example 2

Convert \(2\)m³ to cm³.

Working

\[1\text{m}^3 = 100^3 = 1\,000\,000\text{cm}^3\]cube the length conversion factor
\[2 \times 1\,000\,000\]multiply by the number of cubic metres
\[= 2\,000\,000\text{cm}^3\]state the answer

Example 3

Convert \(2500\)cm³ to litres.

Working

\[1 \text{ litre} = 1000\text{cm}^3\]use the capacity conversion
\[2500 \div 1000\]divide to convert
\[= 2.5 \text{ litres}\]state the answer

Common mistakes

  • Using the length factor for area.

    1m² is 10 000cm², not 100cm². The factor must be squared.

  • Using the squared factor for volume.

    Volume needs the factor cubed, so 1m³ is 1 000 000cm³.

  • Dividing when you should multiply.

    Converting to a smaller unit gives a larger number.

  • Confusing millilitres with cubic metres.

    1ml is 1cm³, not 1m³.

Exam tips

  • Sketch the square or cube and label the sides to derive the factor.
  • Square the factor for area, cube it for volume.
  • Check the answer is larger when converting to smaller units.
  • Remember 1ml = 1cm³ for capacity questions.

Key terms

Conversion factor
The number relating two units.
Capacity
The amount a container can hold.
Cubic
Involving three dimensions multiplied.
Litre
A unit of capacity equal to 1000cm³.

Related topics

Written and reviewed against the current AQA, Edexcel and OCR specifications. Spotted an error? Let us know.