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Britain & the wider world: 1745 -1901
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Maths
3 Dec 2025
173
4 pages
user7650 @2.legit.to.quit
Ever wondered how to work out the space inside a tin can or the amount of material needed... Show more
The area of a circle uses the formula πr², where you multiply the radius by itself, then by π (roughly 3.14). This becomes your foundation for calculating cylinder volumes.
For cylinder volume, you're essentially stacking circles on top of each other. Calculate the circle's area first, then multiply by the height or length. The formula becomes π × r² × height.
When dealing with sector cylinders (like a slice of cake), multiply your answer by the angle over 360. For example, if you have a 90° sector, multiply by 90/360 or ¼.
Quick Tip Always square the radius first, then multiply by π and height - this order prevents calculation errors!
Hollow cylinders (like tubes) need you to subtract the inner volume from the outer volume. Calculate the larger cylinder's volume, then subtract the smaller inner cylinder's volume.
Cone volume uses the formula ⅓ × base area × vertical height. Notice it's exactly one-third of a cylinder with the same base and height - this makes it easier to remember.
The key difference between cones and cylinders is that factor of ⅓ for cones. Everything else follows the same pattern of finding the circular base area first.
Remember Cones are always one-third the volume of cylinders with identical bases and heights!
Sphere volume uses ⁴⁄₃πr³, which means you cube the radius (multiply it by itself three times), then multiply by π and ⁴⁄₃. It's trickier than other shapes but follows a clear pattern.
When calculating cylinder surface area, imagine unfolding a Pringles tube. You get one rectangle (the curved side) plus two circles (top and bottom).
The process breaks down simply find the circumference, multiply by height for the rectangle, calculate the circle area and double it, then add everything together.
Visual Trick Picture peeling the label off a tin can - that rectangle plus the two circular ends gives you the total surface area!
For cylinder surface area, you need two key measurements circumference and circle area .
The curved surface becomes a rectangle with width equal to the circumference and height equal to the cylinder's height. The top and bottom are simply two identical circles.
Your final formula combines these (circumference × height) + (2 × circle area). This systematic approach works for any cylinder size.
Pro Tip Always draw a quick sketch of the "unfolded" shape - it helps you visualise what you're calculating and prevents missing any surfaces!
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.
You can download the app from Google Play Store and Apple App Store.
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
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Transform this note into: ✓ 50+ Practice Questions ✓ Interactive Flashcards ✓ Full Mock Exam ✓ Essay Outlines
Explore key concepts in circle geometry, including formulas for circumference and area, the significance of Pi (π), and data representation through two-way tables. This summary covers essential calculations and properties of circles, making it a valuable resource for Year 8 students. Perfect for quick revision and understanding of mathematical relationships.
MathsThis 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.
MathsExplore 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.
MathsExplore 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.
MathsComprehensive 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.
MathsExplore 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.
MathsQuotes from every main character
English LiteratureApp Store
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
user7650
@2.legit.to.quit
Ever wondered how to work out the space inside a tin can or the amount of material needed to wrap a cylinder? Understanding volumes and surface areas of 3D shapes is essential for maths exams and surprisingly useful in real... Show more
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Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
The area of a circle uses the formula πr², where you multiply the radius by itself, then by π (roughly 3.14). This becomes your foundation for calculating cylinder volumes.
For cylinder volume, you're essentially stacking circles on top of each other. Calculate the circle's area first, then multiply by the height or length. The formula becomes π × r² × height.
When dealing with sector cylinders (like a slice of cake), multiply your answer by the angle over 360. For example, if you have a 90° sector, multiply by 90/360 or ¼.
Quick Tip: Always square the radius first, then multiply by π and height - this order prevents calculation errors!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Hollow cylinders (like tubes) need you to subtract the inner volume from the outer volume. Calculate the larger cylinder's volume, then subtract the smaller inner cylinder's volume.
Cone volume uses the formula ⅓ × base area × vertical height. Notice it's exactly one-third of a cylinder with the same base and height - this makes it easier to remember.
The key difference between cones and cylinders is that factor of ⅓ for cones. Everything else follows the same pattern of finding the circular base area first.
Remember: Cones are always one-third the volume of cylinders with identical bases and heights!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Sphere volume uses ⁴⁄₃πr³, which means you cube the radius (multiply it by itself three times), then multiply by π and ⁴⁄₃. It's trickier than other shapes but follows a clear pattern.
When calculating cylinder surface area, imagine unfolding a Pringles tube. You get one rectangle (the curved side) plus two circles (top and bottom).
The process breaks down simply: find the circumference, multiply by height for the rectangle, calculate the circle area and double it, then add everything together.
Visual Trick: Picture peeling the label off a tin can - that rectangle plus the two circular ends gives you the total surface area!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
For cylinder surface area, you need two key measurements: circumference and circle area .
The curved surface becomes a rectangle with width equal to the circumference and height equal to the cylinder's height. The top and bottom are simply two identical circles.
Your final formula combines these: (circumference × height) + (2 × circle area). This systematic approach works for any cylinder size.
Pro Tip: Always draw a quick sketch of the "unfolded" shape - it helps you visualise what you're calculating and prevents missing any surfaces!
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.
You can download the app from Google Play Store and Apple App Store.
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
3
Smart Tools NEW
Transform this note into: ✓ 50+ Practice Questions ✓ Interactive Flashcards ✓ Full Mock Exam ✓ Essay Outlines
Explore key concepts in circle geometry, including formulas for circumference and area, the significance of Pi (π), and data representation through two-way tables. This summary covers essential calculations and properties of circles, making it a valuable resource for Year 8 students. Perfect for quick revision and understanding of mathematical relationships.
MathsThis 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.
MathsExplore 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.
MathsExplore 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.
MathsComprehensive 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.
MathsExplore 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.
MathsQuotes from every main character
English LiteratureApp Store
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
Sociology