Circles Worksheets, Questions and Revision

Circles Worksheets, Questions and Revision

GCSE 4 - 5KS3AQAEdexcelOCRWJECFoundationAQA 2022Edexcel 2022OCR 2022WJEC 2022

Circles

Circles appear everywhere in maths. Mathematicians just can’t get enough of them.

Here, we’re going to introduce a few of the terms used to describe parts of a circle, and then we’re going to look at calculating the area and perimeter/circumference of a circle. The terms we’ll need are shown on the diagram and described in further detail below.

Level 4-5 GCSE KS3 AQA Edexcel OCR WJEC
circles key terms

Key Circle Terms

  • The circumference is the outside edge of the circle.
  • A diameter is a straight line going straight through the centre of the circle and touching the circumference at each end.
  • A chord is a straight line joining any two parts of the circumference.
  • A segment is the area bound by the circumference and a chord.
  • An arc is a section of the circumference.
  • A radius (plural radii, pronounced “ray-dee-eye”) is a straight line joining the centre to the circumference.
  • A sector is the area bound by two radii and an arc – like a pizza slice.
  • A tangent is a straight line that touches the circumference at a single point.
circles key terms
Level 4-5 GCSE KS3 AQA Edexcel OCR WJEC

Area and Circumference of a Circle

Area of a circle =\textcolor{red}{\pi} \textcolor{blue}{r}^2

Circumference of a circle =\textcolor{red}{\pi} \textcolor{green}{d} = 2\textcolor{red}{\pi}\textcolor{blue}{r}

Where \textcolor{blue}{r} is the radius, \textcolor{green}{d} is the diameter, and \textcolor{red}{\pi} is a very special number with a specific value of 3.14159265... (3.14 to 2 dp).

Level 4-5 GCSE KS3 AQA Edexcel OCR WJEC
Level 4-5 GCSE KS3 AQA Edexcel OCR WJEC
area of a circle example question

Example 1: Area of a Circle

Below is a circle with centre C and radius 3.2 cm.

Find the area of the circle to 1 dp.

[2 marks]

area of a circle example question

Formula: \text{Area }=\pi r^2.

We know the radius is 3.2, so we have

r = 3.2

So, using \pi on our calculator, we get

\text{Area }=\pi \times 3.2^2=32.169...=32.2\text{cm}^2
Level 1-3 GCSE KS3 AQA Edexcel OCR WJEC
circumference of a circle example question

Example 2: Finding the Circumference

Below is a circle with centre C and radius 12cm.

Find the circumference of this circle.

Leave your answer in terms of \pi.

[1 mark]

circumference of a circle example question

 

Formula: \text{Circumference }=\pi d

Where d is the diameter.

We know the radius =12

So, we must double the radius to get the diameter.

\text{diameter }=2\times \text{radius}

12 \times 2 = 24

Now we can find the circumference

\text{circumference }=24\times \pi=24\pi\text{ cm}

Level 1-3 GCSE KS3 AQA Edexcel OCR WJEC

Example Questions

The formula for circumference is \pi d, so we get

 

\text{circumference }=\pi \times 8.4=\dfrac{42}{5}\pi\text{ mm}

 

The circumference is the distance around the outside, so its units are the same as those of the diameter.

 

b) The formula for area is \pi r^2, so firstly we have to get the radius by halving the diameter:

 

r=8.4\div 2=4.2

 

Then we get

 

\text{area }=\pi \times 4.2^2=55.417...=55.4\text{ mm}^2\text{ (3sf)}

 

Area of shapes is always measured in “squared” units. Circles are no exception.

\text{Area}=\pi r^2 = \pi \times 5^2= 25\pi \text{ cm}^2

The formula for area is

 

\text{Area }=\pi r^2

 

In this case, we have \text{area}=200 and r=x. So, putting these values into the formula above, we get the equation

 

200=\pi x^2

 

We can now rearrange this equation to find x. Firstly, divide by \pi to get

 

\dfrac{200}{\pi}=x^2

 

Then, to find out the value of x, square root both sides

 

x=\sqrt{\dfrac{200}{\pi}}=7.97...=8.0\text{ cm (1dp)}

We know the formula we need is

\text{Circumference }=\pi d

We also know that the circumference is 120 and d is, in this case, x. So, filling it in those things that we have into the formula, we get

120=\pi \times x

Now we have an equation we can solve. We want x, so if we divide both sides by \pi, we get

\dfrac{120}{\pi} = x

Put this into a calculator and we get: x=38.2 cm, to 3sf.

Worksheet and Example Questions

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(NEW) Circles - The basics Exam style questions - MME

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