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Lesson 4 of 16

Circumference of a circle

I can use the relationship C=πd to calculate unknown lengths in contexts involving the circumference of circles.

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Lesson 4 of 16
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Circumference of a circle

I can use the relationship C=πd to calculate unknown lengths in contexts involving the circumference of circles.

Download all

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Lesson details

Key learning points

  1. The formula can be used to find the circumference when you know the diameter.
  2. The formula can be used to find the circumference when you know the radius.
  3. The formula can be used to find the radius or diameter when you know the circumference.
  4. These answers will be rounded to an appropriate degree of accuracy.
  5. For the answer to be exact it needs to be left in terms of π.

Keywords

  • Circumference - The circumference of a circle is the perimeter of the circle.

  • Radius - The radius of a circle is any line segment that joins the centre of a circle to its edge.

  • Diameter - The diameter of a circle is any line segment that starts and ends on the edge of the circle and passes through the centre.

Common misconception

When writing answers in terms of π, pupils may think that π is the units.

π is a constant and makes up part of the numerical component of the answer. Units (such as square metres) still need to be stated.

Remind pupils to not round any numbers until they reach a final solution and how to recall previous answers on a scientific calculator by using the 'Ans' button.
Teacher tip

Licence

This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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Prior knowledge starter quiz

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6 Questions

Q1.
Which part of the circle is labelled?

An image in a quiz
circumference
Correct answer: diameter
radius

Q2.
If a circle has a diameter of 12 cm then its radius will be cm.

Correct Answer: 6, six, 6cm, 6 cm

Q3.
$$\pi$$ is the ratio between which two parts of a circle?

the radius and diameter
the radius and circumference
Correct answer: the diameter and circumference

Q4.
Which two formulae can be used to calculate the circumference of a circle?

Correct answer: $$C = \pi d$$
$$C = 2\pi d$$
$$C = \pi r$$
Correct answer: $$C = 2\pi r$$

Q5.
A circle with diameter 12 cm has a circumference of cm.

6$$\pi$$
Correct answer: 12$$\pi$$
24$$\pi$$

Q6.
A circle with radius 20 cm has a circumference of cm.

10$$\pi$$
20$$\pi$$
Correct answer: 40$$\pi$$

Assessment exit quiz

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6 Questions

Q1.
Which part of the circle is labelled?

An image in a quiz
Correct Answer: circumference

Q2.
A circle with a diameter of 6 cm has a circumference of cm, when rounded to 1 decimal place.

Correct Answer: 18.8

Q3.
The circumference of the circle is cm, when rounded to 3 significant figures.

An image in a quiz
Correct Answer: 25.1

Q4.
Which calculation would find the radius of a circle with circumference 20 cm?

$$20 \div $$ $$1 \over 2$$ $$\pi$$
$$20 \div \pi$$
Correct answer: $$20 \div 2\pi$$

Q5.
The circumference of a circle is 30 cm. The diameter of the circle is cm, when rounded to 1 decimal place.

Correct Answer: 9.5

Q6.
Starting with the smallest, sort the circles in ascending order of size.

1 - a circle with circumference 10 cm
2 - a circle with diameter 4 cm
3 - a circle with radius 3 cm

Lesson appears in

UnitMaths / Perimeter, area and volume

Maths

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