Circumference and area of circles
A clear starting point, worked steps and space to practise.
Start here
A circle’s circumference is the distance around it. Its area is the space inside it.
Check units: circumference uses cm; area uses cm². Do not use the diameter in a formula that requires the radius.
1 Work through these steps
- Identify the radius or diameter.
- Use diameter = 2 × radius.
- For circumference use 2πr; for area use πr².
- Keep π exact unless rounding is requested.
2 Follow a worked example
A circle has radius 3 cm. Find its circumference and area in terms of π.
- Diameter = 6 cm.
- Circumference = 2 × π × 3 = 6π cm.
- Area = π × 3² = 9π cm².
3 Try it yourself
Show each step on paper or open Working out. Then check the answer.
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Find the area of a circle with diameter 10 m.
Check answer 1
Answer: 25π m²
The radius is 5 m; area = π × 5² = 25π m².
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Working out
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Check your understanding
Explain the worked example in your own words. Say why the method works, not just what the answer is.
Skills and explanation links
Key ideas taught here
- A circle’s circumference is the distance around it. Its area is the space inside it.
- Check units: circumference uses cm; area uses cm². Do not use the diameter in a formula that requires the radius.
Method and checking
Optional recap: related Maths skills
These earlier examples revisit background skills. Start with the topic example and practice above.
Useful vocabulary
- area
- The space inside a flat shape.
- perimeter
- The distance around a shape.
- square unit
- A unit used to measure area.
- formula
- A rule used to calculate efficiently.
Rules for these related skills
Area measures inside space; perimeter measures around the edge.
Area of a rectangle = length x width.
Area uses square units such as square cm or square m.
Find the perimeter of a 5 cm by 3 cm rectangle.
- Perimeter is around the outside.
- 5 + 3 + 5 + 3 = 16.
- Answer: 16 cm.
Find the area of a 6 m by 4 m rectangle.
- Area = length x width.
- 6 x 4 = 24.
- Answer: 24 square metres.
Find the area of a triangle with base 8 cm and height 5 cm.
- Triangle area = base x height / 2.
- 8 x 5 = 40.
- 40 / 2 = 20 square centimetres.
A garden bed is 7 m long and 2 m wide. How much soil area is covered?
- Use area, not perimeter.
- 7 x 2 = 14.
- The area is 14 square metres.
More visual models and everyday examples
Each everyday example has its own information and model. Use its stated values rather than copying values from another question.
Concept example. The story examples below have their own diagrams.
Count one row, then multiply by the number of rows.
For parents and teachers
- Ask your child to explain the method aloud before writing the answer.
- Use a real-life context at home, such as shopping, cooking, sport scores, maps or timetables.
- Praise clear working and checking, not only speed.
- Ask your child to write the formula or rule first, then substitute values carefully.
Practise choosing a method from the information in the question. The examples here are Pi Leo Academy learning activities. Official NAPLAN testing takes place in Years 3, 5, 7 and 9; a topic appearing in these notes does not mean it is tested in NAPLAN.
These notes provide guided examples and practice; they do not certify completion of every curriculum requirement.