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Circle Circumference Challenge Problems

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Circle Circumference Challenge Problems

Use π = 3.14 for every question. Show your working and include units in your answers.

Circumference in everyday situations

Circumference is the distance around a circle. Use the measurements given in each question to calculate circumference where needed.

1.A scooter wheel has a diameter of 48 cm. How far does the scooter travel, in metres, when the wheel turns 75 complete times?
2.A circular flower bed has a radius of 1.8 m. A border is made from edging pieces that are each 30 cm long. How many pieces are needed to go all the way around the bed?
3.A circular fountain has a circumference of 50.24 m. What is its radius?
4.A circular patio has a diameter of 9.5 m. Paving trim costs £8.40 per metre. How much will trim cost for the whole edge?

Multi-step circumference challenges

Take care to use the correct fraction of the circumference when a circle is divided into equal parts.

5.A round cake has a diameter of 28 cm and is cut into 7 equal slices. Find the length of the curved edge of one slice.
6.A circular table has a radius of 68 cm. Another has a radius of 52 cm. How much longer is the circumference of the larger table?
7.A dog runs on a circular exercise track with a circumference of 125.6 m. If it completes 85 laps, what total distance has it run in kilometres?
8.A circular pond has a circumference of 37.68 m. Its radius is increased by 25%. What is the new circumference?

Reasoning and problem solving

Use clear calculations to support your reasoning.

9.Explain what happens to a circle’s circumference when its radius is tripled. Use a circle with an original radius of 4 cm to support your explanation with calculations.
10.A circular badge must fit exactly inside a square that is 15 cm along each side. What is the circumference of the largest circle that can fit inside the square?

3 printable pages

  • A labelled circle showing radius, diameter and circumference, followed by everyday circumference calculations.

    Page 1

  • Multi-step challenges involving arcs, comparing circumferences, repeated rotations and a changing radius.

    Page 2

  • Reasoning about how circumference changes with radius and finding the circumference of a circle inside a square.

    Page 3

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