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Year 8

Multiplicative relationships in circles

I can recognise that there is a constant multiplicative relationship (π) between the diameter and circumference of a circle.

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New
New
Year 8

Multiplicative relationships in circles

I can recognise that there is a constant multiplicative relationship (π) between the diameter and circumference of a circle.

Download all resources
Share activities with pupils

Lesson details

Key learning points

  1. There is a multiplicative relationship between the radius and diameter of a circle.
  2. The ratio between the diameter and circumference of a circle is always the same.
  3. That ratio is called π and it is an irrational number.
  4. The formula for the circumference of a circle is C = πD.
  5. Using the definition of the diameter you can also write this as C = 2πr.

Common misconception

Pupils may think that the π symbol represents a variable, similar to letters such as r and d.

Reiterate the difference between variables and constants. Explain that while the radius may differ between circles, π is always the same.

Keywords

  • 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.

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

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

Pupils can re-enact the practical demonstration wrapping string around a cylindrical object, cutting it to the length of the circumference and then checking if the string is just over three times the diameter for their object too.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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Starter quiz

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6 Questions

Q1.
Round 50.26548246 to 1 decimal place.
Correct Answer: 50.3
Q2.
Round 3.14159265 to 3 significant figures.
Correct Answer: 3.14
Q3.
The perimeter of the parallelogram is units.
An image in a quiz
8
12
Correct answer: 16
24
Q4.
Select the rectangle with the largest perimeter.
Correct Answer: An image in a quiz
An image in a quiz
An image in a quiz
An image in a quiz
Q5.
$$a : b = 1 : 3$$. Find the value of $$b$$ when $$a = 6$$.
Correct Answer: 18, eighteen
Q6.
$$a : b = 1 : 3$$. Find the value of $$a$$ when $$b = 6$$.
Correct Answer: 2, two

Exit quiz

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6 Questions

Q1.
Which part of the circle is labelled?
An image in a quiz
arc
circumference
diameter
Correct answer: radius
Q2.
The of a circle is the perimeter of the circle.
Correct Answer: circumference
Q3.
If a circle has a radius of 12 cm then its diameter will be cm.
Correct Answer: 24, twenty four, 24 cm, 24cm
Q4.
Which symbol represents the ratio between the diameter and circumference of a circle?
$$\alpha$$
$$\beta$$
$$\Delta$$
Correct answer: $$\pi$$
Q5.
Which are the first three digits of $$\pi$$?
Correct Answer: 3.14
Q6.
A circle with diameter 10 cm has a circumference of cm.
5$$\pi$$
Correct answer: 10$$\pi$$
20$$\pi$$