# Find the Area of a Sector of a Circle

In this worksheet, students will find the areas of sectors of circles from a given radius.

Key stage:  KS 3

Curriculum topic:   Geometry and Measures

Curriculum subtopic:   Derive and Apply Formulae

Difficulty level:

#### Worksheet Overview

In this activity, we will be calculating the area of sectors of a circle.

You will need a scientific calculator.

A sector is a portion or a part of a circle.

To find the area of a circle we square the radius and multiply it by pi

What is pi (π) in numbers?

Pi is an infinite number, and you can use a function on your calculator to input the number.

Here is the start of it  3.14159265359...

We write it like this in short:

Area of a circle = π r2

To find a sector we are finding a portion of this formula.

Let's look at a question.

Example

Find the area of a sector of a circle with radius 6 cm.

Angle at the centre is 45

Area = π r2 x 45 ÷ 360

This is because we want 45/360ths of a full circle area.

=  π × 62 x 45/360

= π × 36 x 45 ÷ 360

= 14.1 cm2 (to 1 dp)

Remember, in this activity, you need to use a scientific calculator to calculate pi correctly.

You can access one of these online if you do not have one.

Let's do some questions like this!

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