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Sector Areas and Arc Lengths

Sector Areas and Arc Lengths

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Lesson

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8 minute activity

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Sector of a circle with centre O, two radii, central angle theta, and arc length L labelled

A sector is a slice of a circle made from two radii and the arc between them. The diagram shows the central angle θ\thetaθ and the curved edge, which is the arc length LLL.

A full circle is 360∘360^{\circ}360∘, so a sector with angle θ\thetaθ is the fraction θ360\frac{\theta}{360}360θ​ of the whole circle. This same fraction tells you how much of the full area and full circumference you are using.

Questions

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30 exam-style questions

Practice questions

Question 1

2 marks

The diagram shows a sector, centre OOO. The radius of the circle is 8 cm. The angle of the sector is 150∘150^\circ150∘.

Flashcards

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22 flashcards

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For a circle with radius rrr, what is the area formula?

Sector Areas and Arc Lengths Revision Guide

  1. GCSE
  2. /Maths
  3. /Sector Areas and Arc Lengths

Revision notes for WJEC GCSE Maths Sector Areas and Arc Lengths: explanations and worked examples.

Practise questions

1 of 5

A sector has a central angle of 90°90°90°. What fraction of a full circle is the sector?