Australian Curriculum v9 / ACiQ Year 7 Mathematics - Unit 0 - Radius, diameter, circumference and pi

Radius, diameter, circumference and pi

Investigate and describe the relationships among a circle's radius, diameter, circumference and pi.

Updated 2026-07-24 - 6 min read

Investigate and describe the relationships among a circle's radius, diameter, circumference and pi. This draft teaching resource is aligned to the cited Year 7 content descriptions and still requires named human curriculum approval.

Name what each length, angle, coordinate or view represents before choosing a formula or transformation; the diagram and units are part of the reasoning.

1. Investigate circle relationships

A diameter is two radii through the centre. Across circles of different sizes, circumference divided by diameter stays close to π.

Text-equivalent representation: Circle text model: centre O; radius is a segment from O to the edge; diameter is a straight segment from edge to edge through O and contains two radii; circumference is the distance once around.

Decision check: Apply this lesson's rule to the worked example: Use d = 2r and investigate C/d ≈ π as a measured relationship, allowing for measurement variation. Identify the exact value, label or property that satisfies the rule.

Worked examples with complete reasoning

Worked example 1

Question: A circle has radius 4 cm. Find its diameter.

  1. The diameter is twice the radius.
  2. d = 2 × 4 = 8 cm.

Answer: 8

Check: The radius reaches from centre to edge; the diameter crosses the full circle through the centre.

Worked example 2

Question: During a circle investigation, a student measures an object with diameter 10 cm. Which circumference record is most consistent with C ÷ d being close to π?

  1. Across measured circles, circumference is a little more than three times the diameter.
  2. about 31 cm gives a circumference-to-diameter ratio close to π.

Answer: about 31 cm

Check: Compare each proposed circumference with a little more than three diameters; treat the result as measurement evidence, not an exact formula exercise.

Worked example 3

Question: Circle B’s diameter is 16 cm and Circle A’s is 8 cm. How many times Circle A’s circumference is Circle B’s circumference?

  1. Circumference is proportional to diameter because C/d is constant.
  2. 16 ÷ 8 = 2.

Answer: 2

Check: The same scale factor links diameters and circumferences.

Method map for this topic

  1. Investigate circle relationships: Use d = 2r and investigate C/d ≈ π as a measured relationship, allowing for measurement variation.

Common mistakes and how to correct them

  • radius diameter: Not yet. The radius reaches from centre to edge; the diameter crosses the full circle through the centre. Recheck the radius diameter step, then try again.
  • diameter radius: Not yet. Halve the diameter. Recheck the diameter radius step, then try again.
  • circumference diameter: Not yet. Compare each proposed circumference with a little more than three diameters; treat the result as measurement evidence, not an exact formula exercise. Recheck the circumference diameter step, then try again.
  • pi ratio: Not yet. Use the same units so they cancel in the ratio. Recheck the pi ratio step, then try again.
  • circle vocabulary: Not yet. Sketch and label a circle if the terms are easy to swap. Recheck the circle vocabulary step, then try again.
  • circle scaling: Not yet. The same scale factor links diameters and circumferences. Recheck the circle scaling step, then try again.

Practice

  1. A circle has radius 4 cm. Find its diameter.
  2. A circle has radius 7.5 cm. Find its diameter.
  3. During a circle investigation, a student measures an object with diameter 10 cm. Which circumference record is most consistent with C ÷ d being close to π?
  4. During a circle investigation, a student measures an object with diameter 12 cm. Which circumference record is most consistent with C ÷ d being close to π?
  5. Circle B’s diameter is 16 cm and Circle A’s is 8 cm. How many times Circle A’s circumference is Circle B’s circumference?
  6. Circle B’s diameter is 15 cm and Circle A’s is 5 cm. How many times Circle A’s circumference is Circle B’s circumference?

<details> <summary>Answers and reasoning</summary>

  1. 8 — The diameter is twice the radius. d = 2 × 4 = 8 cm.
  2. 15 — The diameter is twice the radius. d = 2 × 7.5 = 15 cm.
  3. about 31 cm — Across measured circles, circumference is a little more than three times the diameter. about 31 cm gives a circumference-to-diameter ratio close to π.
  4. about 38 cm — Across measured circles, circumference is a little more than three times the diameter. about 38 cm gives a circumference-to-diameter ratio close to π.
  5. 2 — Circumference is proportional to diameter because C/d is constant. 16 ÷ 8 = 2.
  6. 3 — Circumference is proportional to diameter because C/d is constant. 15 ÷ 5 = 3.

</details>

Checklist and vocabulary

| Skill | Observable evidence | | --- | --- | | relate radius diameter | Use the relationship that the diameter is twice the radius. | | investigate circumference diameter pi | Calculate and interpret circumference divided by diameter as approximately pi. | | describe circle scaling relationship | Describe how circumference changes when diameter is scaled, using measured-circle evidence. |

Retrieval prompts

  • State the defining relationship for each method above without looking.
  • Give one example where two visually similar representations mean different things.
  • Diagnose one misconception from the list and explain the first corrective step.
  • Name a check that is independent of simply repeating the same calculation.

Teach-back and self-check

Close the worked examples and explain radius, diameter, circumference and pi as if you were helping another Year 7 student. Begin by naming the clue that tells you which relationship, representation or operation is needed. Then show one complete example with labels and units where they matter. At each line, explain what stayed equivalent and why the next step is allowed.

Use this four-part check before calling the method secure:

  1. Identify: What information is given, and what must be found or justified?
  2. Represent: Which number line, diagram, table, expression, graph or organised list makes the relationship visible?
  3. Reason: Which rule connects the representation to the required answer?
  4. Verify: Can you check by estimation, substitution, an inverse operation, a second representation or the original context?

If the explanation depends on “I just knew”, return to the method map and name the missing decision. A durable method is one you can explain, check and use in a changed context after a delay.

Transfer task

Sketch or describe a real object or layout that uses radius, diameter, circumference and pi. Label every necessary dimension, coordinate, axis or view, solve the stated problem, and name one limitation of the representation.

Sources