  # 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. 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. 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 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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