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Find the Length of an Arc

In this worksheet, students will learn the formula for finding the length of an arc and will be able to apply it.

'Find the Length of an Arc' worksheet

Key stage:  KS 4

Year:  GCSE

GCSE Subjects:   Maths

GCSE Boards:   AQA, Eduqas, OCR, Pearson Edexcel,

Curriculum topic:   Geometry and Measures, Mensuration

Curriculum subtopic:   Mensuration and Calculation Perimeter Calculations

Difficulty level:  

Worksheet Overview

Do you need an arc?

I Noah guy.....

Apart from the ark that Noah built, there is another kind.


As you can see from the diagram below, an arc is a part of the circumference of a circle.


An arc


Probably the only time you will need to calculate the length of an arc is in maths lessons.  (Unless Noah offers you a job)

Maths is a little bit like building Noah's ark.

It is easy if you read the instructions carefully. 

Instructions in maths come in the form of a formula.


Being part of a circle, pi pi  is involved of course.


Circumference of a circle is π  x diameter  (πd)

Since an arc is part of the circumference, it makes sense to use this as part of our calculation:


Length of an arc = angle ÷ 360 x π x diameter


Generally in maths questions, you're given the radius of the circle - you could double the radius to get the diameter or the formula applied could be:

Length of an arc = angle ÷ 360 x 2 x π x radius          


Remember you can use the π button on your calculator or use the values 3.14 or 3.142 in your calculations.

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