Geometry and measurement

Circumference of a Circle Practice

Find the distance around a circle from radius or diameter, work backwards from circumference, and solve wheel and boundary problems.

Grades 7–8 practice · 6 questions · Free to print · Answers included

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Make sense of the method

Circumference is the distance around a circle. Every circle has the same circumference-to-diameter ratio, π, so C = πd = 2πr.

Circumference uses length units, unlike circle area. These questions give exact answers in terms of π and use 3.14 only for the requested estimates.

  1. Identify whether the given length is a radius or a diameter.
  2. Use C = πd or C = 2πr.
  3. Keep π until the final step unless an approximation is requested.
  4. For an inverse problem, divide circumference by π to get diameter, then halve if you need radius.

A worked example

Find the circumference of a circle with diameter 8 cm. Give an exact answer and use π ≈ 3.14 for an estimate.

Example diameterCircle. Diameter: 8 cm. Drawing not to scale.8 cmDrawing not to scale
Example diameter
  1. Use C = πd because the diameter is given.
  2. C = π × 8 = 8π cm.
  3. 8 × 3.14 = 25.12 cm.

8π cm, approximately 25.12 cm.

Try the worksheet

Start with the first two questions, then build toward the final challenge. Show your method with calculations, drawings or a short explanation. These are practice questions with published answers, not a full-topic readiness check.

  1. Build the foundation

    1.A circle has diameter 6 m. Find its circumference exactly and using π ≈ 3.14.

    Diameter 6 mCircle. Diameter: 6 m. Drawing not to scale.6 mDrawing not to scale
    Diameter 6 m
    Show your work on paper.

  2. Build the foundation

    2.A circular pond has radius 4.5 m. Find its circumference in terms of π and using 3.14.

    Pond radiusCircle. Radius: 4.5 m. Drawing not to scale.4.5 mDrawing not to scale
    Pond radius
    Show your work on paper.

  3. Strengthen your method

    3.A circle has circumference 37.68 cm, calculated using π ≈ 3.14. Recover its diameter and radius.

    Show your work on paper.

  4. Strengthen your method

    4.A bicycle wheel has diameter 70 cm. How far does it travel in 20 complete revolutions without slipping? Use π ≈ 3.14 and give the answer in metres.

    Wheel diameterCircle. Diameter: 70 cm. Drawing not to scale.70 cmDrawing not to scale
    Wheel diameter
    Show your work on paper.

  5. Apply and explain

    5.A semicircular garden has radius 7 m. Find its complete perimeter, including the straight edge. Give an exact answer and use 3.14 for an estimate.

    Show your work on paper.

  6. Apply and explain

    6.A running track has two straight sections of 40 m joined by two semicircular ends of radius 10 m. Sketch the track and find the distance for 3 laps using π ≈ 3.14.

    Show your work on paper.
Download free worksheetPDF

Worked answers

Try the questions first. Then compare the reasoning, not just the final result.

Show all six worked solutions

  1. 1. 6π m, approximately 18.84 m.

    1. C = πd = 6π m.
    2. 6 × 3.14 = 18.84 m.

  2. 2. 9π m, approximately 28.26 m.

    1. Diameter = 2 × 4.5 = 9 m.
    2. C = π × 9 = 9π m.
    3. Approximation: 9 × 3.14 = 28.26 m.

  3. 3. Diameter 12 cm; radius 6 cm.

    1. d = C ÷ π = 37.68 ÷ 3.14 = 12 cm.
    2. r = d ÷ 2 = 6 cm.
    3. Check: 3.14 × 12 = 37.68 cm.

  4. 4. 43.96 m.

    1. One revolution travels one circumference: 3.14 × 70 = 219.8 cm.
    2. Twenty revolutions: 219.8 × 20 = 4396 cm.
    3. Convert centimetres to metres: 4396 ÷ 100 = 43.96 m.

  5. 5. 7π + 14 m, approximately 35.98 m.

    1. The curved boundary is half a circumference: (2π × 7) ÷ 2 = 7π m.
    2. The straight boundary is the diameter: 14 m.
    3. Total perimeter = 7π + 14 m ≈ 21.98 + 14 = 35.98 m.

  6. 6. 428.4 m.

    1. The two semicircular ends together make one full circle.
    2. One lap = 2 × 40 + 2π × 10 = 80 + 20π m.
    3. Using 3.14 gives 142.8 m per lap.
    4. Three laps = 3 × 142.8 = 428.4 m.

Mistakes worth catching

Using πr instead of 2πr.

A diameter is two radii, so the radius formula needs the factor 2.

Omitting the straight edge of a semicircle.

Complete perimeter includes the curved half-circle and its diameter.

Rounding each intermediate calculation.

Keep the exact expression or full precision until the requested final estimate.

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Skills covered

Geometry and measurement

  • Calculate circumference from a radius or diameter and work backwards.
  • Apply distance-around reasoning to wheels and boundaries.

Choose this practice by the skills you need. Grade placement and strand names vary between school systems; one worksheet covers selected skills rather than every expectation in a topic.

Related practice

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Created by Gradulo · Updated September 9, 2026 · Free for personal and classroom practice.
Circumference Worksheets with Worked Answers | Gradulo