Circles, arcs and sectors Edexcel International GCSE Mathematics A revision
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In plain words
Wrap a tape round any circle, divide by the distance across, and you always get the same number: a little over 3. That number is π. Everything about circles comes from it.
Three things to know
- Circumference = π × diameter = 2πr. Area = πr².
- An arc is part of the circumference, and a sector is part of the area. For an angle θ at the centre, each is θ/360 of the whole: arc = θ/360 × 2πr, sector area = θ/360 × πr².
- If you're given the diameter, halve it before using πr².
Worked example
Find the area of a sector of radius 6 cm with an angle of 60°.
- The sector is 60/360 of the whole circle, which is one sixth.
- Area = 60/360 × π × 6² = 1/6 × 36π = 6π.
- = 18.8 cm² (to 3 significant figures).
Tips and tricks
- Area has r squared. Circumference doesn't. "Area: r squared" is how to remember which is which.
- Use the π button on your calculator, and round only at the end.
It lands in your notebook with its questions as flashcards.
Circles, arcs and sectors: 5 questions and answers
These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.
What is the formula for the area of a circle?
Radius squared, times π.
A circle has a radius of 3 cm. What is its circumference?
2 × π × 3.
A circle has a diameter of 10 cm. What is its area?
The radius is 5, and 5² = 25.
What fraction of a circle is a sector with an angle of 90°?
90/360.
A sector has radius 4 cm and angle 180°. What is its area?
Half of π × 4².
Quiz
5 questions
Tap an answer and you’ll see straight away whether it’s right, and why.
Worksheet
3 questions, 7 marks. Write your answers on paper, then check them.
Circles, arcs and sectors
Edexcel International GCSE Mathematics A 4MA1 · 7 marks · papermunch.org
Name ______________________________ Date ______________
Find the circumference of a circle of radius 5 cm.[2]
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31.4 cm. 2 × π × 5.
Find the area of a circle of diameter 12 cm.[2]
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113 cm². π × 6².
Find the length of an arc of a circle of radius 9 cm that has an angle of 80° at the centre.[3]
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12.6 cm. 80/360 × 2 × π × 9.
Answers: Circles, arcs and sectors
- 1. 31.4 cm. 2 × π × 5.
- 2. 113 cm². π × 6².
- 3. 12.6 cm. 80/360 × 2 × π × 9.