Circles are everywhere around us, from coins to wheels to... Show more
SociologySign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
250
•
13 Dec 2025
•
Maths Study Guide: Year 8 Topics
Amelia
@milly.13
1 / 4
Area of Circles
Ever wondered how much pizza you're actually getting? The area of a circle tells you exactly that! The magic formula is Area = πr², where π (pi) is roughly 3.14 and r is the radius.
Remember, if you're given the diameter, just divide it by 2 to get the radius. Think of it like cutting a pizza in half - the radius goes from the centre to the edge.
Here's a clever way to understand why the formula works: imagine cutting a circle into sectors (like pizza slices) and rearranging them into a rectangle shape. The length becomes πr and the width becomes r, so the area is πr × r = πr².
Quick Tip: Always check if you're given the diameter or radius - this is the most common mistake students make!
Circumference of Circles
The circumference is simply the distance around the outside of a circle - like measuring the rim of a bicycle wheel. You've got two handy formulas depending on what information you're given.
If you know the diameter, use C = πd. Just multiply π by the diameter and you're sorted! If you only have the radius, use C = 2πr - multiply the radius by 2, then by π.
The brilliant thing about circles is that π is the same for every single circle, no matter how big or small. It's the circumference divided by the diameter, and it's always roughly 3.14.
Pro Tip: When using a calculator, use the π button for more accurate answers rather than typing 3.14!
Finding Missing Measurements and Similar Shapes
Sometimes you'll need to work backwards from the circumference to find the diameter or radius. Simply divide the circumference by π to get the diameter, then halve it for the radius.
Conversion graphs are brilliant tools that help you change one unit into another. They work because the values are directly proportional - as one increases, the other increases at the same rate.
Similar shapes are like identical twins of different sizes! They have the same angles and proportional sides. If one side doubles in length, all sides must double - this consistent change is called the scale factor.
Remember: Similar shapes can be rotated or flipped, but their angles must match perfectly!
Two-Way Tables and Data Representation
Two-way tables are like spreadsheets that help you organise data involving two different variables. Think of them as a grid where rows represent one category and columns represent another.
Reading these tables is straightforward - find where your row and column meet, and that cell shows you the frequency of data that fits both categories. It's like finding a specific seat in a cinema using row and seat numbers.
These tables are incredibly useful for calculating probabilities and spotting patterns in data. They make complex information much easier to understand at a glance.
Study Smart: Practice reading two-way tables by creating your own with data about your classmates' favourite subjects and hobbies!
We thought you’d never ask...
What is the Knowunity AI companion?
Our AI Companion is a student-focused AI tool that offers more than just answers. Built on millions of Knowunity resources, it provides relevant information, personalised study plans, quizzes, and content directly in the chat, adapting to your individual learning journey.
Where can I download the Knowunity app?
You can download the app from Google Play Store and Apple App Store.
Is Knowunity really free of charge?
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
Most popular content in Maths
Most popular content
English - inspector calls quotes and analysis
Quotes from every main character
English Literature10
Can't find what you're looking for? Explore other subjects.
Students love us — and so will you.
4.9/5
App Store
4.8/5
Google Play
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
Maths Study Guide: Year 8 Topics
Amelia
@milly.13
Circles are everywhere around us, from coins to wheels to pizza! Understanding how to calculate their area and circumference is a crucial maths skill you'll use throughout your studies and beyond.
Area of Circles
Ever wondered how much pizza you're actually getting? The area of a circle tells you exactly that! The magic formula is Area = πr², where π (pi) is roughly 3.14 and r is the radius.
Remember, if you're given the diameter, just divide it by 2 to get the radius. Think of it like cutting a pizza in half - the radius goes from the centre to the edge.
Here's a clever way to understand why the formula works: imagine cutting a circle into sectors (like pizza slices) and rearranging them into a rectangle shape. The length becomes πr and the width becomes r, so the area is πr × r = πr².
Quick Tip: Always check if you're given the diameter or radius - this is the most common mistake students make!
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Circumference of Circles
The circumference is simply the distance around the outside of a circle - like measuring the rim of a bicycle wheel. You've got two handy formulas depending on what information you're given.
If you know the diameter, use C = πd. Just multiply π by the diameter and you're sorted! If you only have the radius, use C = 2πr - multiply the radius by 2, then by π.
The brilliant thing about circles is that π is the same for every single circle, no matter how big or small. It's the circumference divided by the diameter, and it's always roughly 3.14.
Pro Tip: When using a calculator, use the π button for more accurate answers rather than typing 3.14!
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Finding Missing Measurements and Similar Shapes
Sometimes you'll need to work backwards from the circumference to find the diameter or radius. Simply divide the circumference by π to get the diameter, then halve it for the radius.
Conversion graphs are brilliant tools that help you change one unit into another. They work because the values are directly proportional - as one increases, the other increases at the same rate.
Similar shapes are like identical twins of different sizes! They have the same angles and proportional sides. If one side doubles in length, all sides must double - this consistent change is called the scale factor.
Remember: Similar shapes can be rotated or flipped, but their angles must match perfectly!
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Two-Way Tables and Data Representation
Two-way tables are like spreadsheets that help you organise data involving two different variables. Think of them as a grid where rows represent one category and columns represent another.
Reading these tables is straightforward - find where your row and column meet, and that cell shows you the frequency of data that fits both categories. It's like finding a specific seat in a cinema using row and seat numbers.
These tables are incredibly useful for calculating probabilities and spotting patterns in data. They make complex information much easier to understand at a glance.
Study Smart: Practice reading two-way tables by creating your own with data about your classmates' favourite subjects and hobbies!
We thought you’d never ask...
What is the Knowunity AI companion?
Our AI Companion is a student-focused AI tool that offers more than just answers. Built on millions of Knowunity resources, it provides relevant information, personalised study plans, quizzes, and content directly in the chat, adapting to your individual learning journey.
Where can I download the Knowunity app?
You can download the app from Google Play Store and Apple App Store.
Is Knowunity really free of charge?
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
9
Smart Tools NEW
Transform this note into: ✓ 50+ Practice Questions ✓ Interactive Flashcards ✓ Full Mock Exam ✓ Essay Outlines
Mock Exam
Quiz
Flashcards
Essay
Similar content
Geometric Volume & Surface Area
Explore essential formulas for calculating the volume and surface area of spheres, cones, and cylinders. This summary includes key equations for the area of a circle and detailed examples to enhance your understanding of geometric shapes. Ideal for students preparing for exams or needing a quick reference.
Maths9
Surface Area of 3D Shapes
This educational resource provides a comprehensive overview of calculating the surface area and volume of various 3D shapes, including cuboids and cylinders. Ideal for Year 8 students, it covers essential formulas and step-by-step examples to enhance understanding of geometric concepts.
Maths7
Year 7 Maths Essentials
Explore key Year 7 maths concepts including Venn diagrams, gradients, LCM, HCF, probability, and algebra. This comprehensive guide covers essential topics such as area, perimeter, angles, and statistics, providing clear explanations and examples to enhance your understanding. Perfect for students looking to strengthen their maths skills.
Maths7
Year 8 Maths Curriculum Overview
Explore the comprehensive Year 8 Mathematics curriculum, covering key topics such as number properties, algebraic manipulation, geometry, statistics, and probability. This summary includes assessment modules, essential skills, and resources for effective learning. Ideal for students preparing for Edexcel exams.
Maths8
GCSE Maths Formulae Guide
Comprehensive formula sheet for Edexcel GCSE Mathematics covering areas, volumes, compound measures, circle formulas, quadratic equations, and trigonometric identities. Essential for exam preparation and quick reference.
Maths9
Perimeter, Area & Volume Formulas
Explore essential formulas for calculating perimeter, area, and volume of 2D and 3D shapes. This summary covers key concepts for KS3 and KS4 students, including practical examples and measurement units. Perfect for revision and exam preparation.
Maths9
Most popular content in Maths
Most popular content
English - inspector calls quotes and analysis
Quotes from every main character
English Literature10
Can't find what you're looking for? Explore other subjects.
Students love us — and so will you.
4.9/5
App Store
4.8/5
Google Play
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user