  # Find the Area of a Sector

In this worksheet, students will learn the formula for finding the area of a sector and be able to apply it. Key stage:  KS 4

GCSE Subjects:   Maths

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

Curriculum topic:   Geometry and Measures, Mensuration

Curriculum subtopic:   Mensuration and Calculation Area Calculations

Difficulty level:   #### Worksheet Overview

When you go to a pizza restaurant, I don't suppose you are wondering where the maths is, do you?

Maybe you do.  I am usually too hungry! Take this humble pizza, where is the maths in that?

The slice you have just cut for yourself (looks a little small to me) is called a sector.

A sector is an area between an arc of a circle at its two radii.

Now to find out how much you have cut you need to find the area of the sector.

As ever there is a formula to do this.

As we are looking a part of a circle is involved of course.

To find the area of a circle we use the formula Πr²  or (π x r x r)

It makes sense to use this to find the sector.

Remember you can use the π button on your calculator or use the value 3.14

Area of a sector =  angle/360 x π x radius x radius      (angle/360 x πr²)

Let's calculate how hungry you are! The radius of the pizza is 6 cm and the angle is 50°

50 ÷ 360 x π x 6 x 6 = 15.71 cm²

To save a lot of writing down in mid calculation, it is best if you use a scientific calculator as you can put the whole formula in at once.

The calculator is clever enough to know the value of pi too.

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