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5
0
A
atty Ali
09/12/2025
Maths
surface area and volume
237
•
9 Dec 2025
•
Surface Area and Volume Formulas
A
atty Ali
@attyali_jgch
1 / 4
Cylinders
Think of a cylinder as a tin can - it's got a circular top and bottom with curved sides connecting them. The volume formula is π r² h, where r is the radius and h is the height.
For surface area, you need to add up all the surfaces: the curved side plus the two circular ends. The formula becomes 2πrh + 2πr². The first part (2πrh) gives you the curved surface, whilst the second part (2πr²) covers both circular ends.
Let's say you've got a cylinder with radius 5cm and height 15cm. For surface area: 2 × π × 5 × 15 + 2 × π × 5² = 628cm². For volume of a water tank with radius 25cm and height 120cm: π × 25² × 120 = 235,500cm³.
Quick tip: Remember that volume always uses cubic units (cm³) whilst surface area uses square units (cm²).
Spheres
A sphere is perfectly round like a football or tennis ball. Unlike other 3D shapes, spheres only need the radius to calculate everything - no height or width measurements required.
The volume formula is (4/3)πr³. For a ball with radius 7cm, you'd get (4/3) × π × 7³ = 436.75cm³. That's quite a lot of space inside!
Surface area uses 4πr². If your sphere has a radius of 10cm, the calculation becomes 4π × 10² = 502.4cm². This formula is much simpler than cylinders because there's only one curved surface to worry about.
Remember: Spheres are the only 3D shape where you don't need to think about separate faces - it's all one smooth surface.
Pyramids
Pyramids have a flat base (usually square) with triangular faces that meet at a point at the top. Think of the Egyptian pyramids, but smaller and with precise measurements!
The volume formula is (length × width × height) ÷ 3. For a pyramid that's 8cm by 6cm at the base and 9cm tall, you'd calculate: (8 × 6 × 9) ÷ 3 = 144cm³. Notice how it's one-third of what a rectangular box would be.
Surface area means adding up all the faces. You need the area of the square base plus all four triangular sides. For a pyramid with base 5cm × 5cm and triangular faces of 20cm² each: base area = 25cm², four triangular faces = 80cm², total = 105cm².
Pro tip: Always remember to divide by 3 for pyramid volume - it's the most common mistake students make!
Cones
A cone looks like an ice cream cone or traffic cone - it has a circular base that tapers to a point. You'll need to know the radius of the base and either the height or slant height.
The volume formula is (1/3)πr²h, where h is the perpendicular height (straight up from base to tip). For a cone with radius 5cm and height 8cm: (1/3) × π × 5² × 8 = 209.3cm³.
Surface area combines the circular base (πr²) with the curved surface (πrl, where l is the slant height). With radius 14cm and slant height 8cm, you'd calculate: π × 14² + π × 14 × 8 = 508cm².
Key point: Make sure you know whether you're given the perpendicular height or slant height - they're different measurements!
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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
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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
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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
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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
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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
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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
Surface Area and Volume Formulas
A
atty Ali
@attyali_jgch
Learning to calculate the volume and surface area of 3D shapes is essential for GCSE maths and real-world applications. These formulas help you work out everything from the amount of paint needed to cover a cylindrical tank to the volume... Show more
Cylinders
Think of a cylinder as a tin can - it's got a circular top and bottom with curved sides connecting them. The volume formula is π r² h, where r is the radius and h is the height.
For surface area, you need to add up all the surfaces: the curved side plus the two circular ends. The formula becomes 2πrh + 2πr². The first part (2πrh) gives you the curved surface, whilst the second part (2πr²) covers both circular ends.
Let's say you've got a cylinder with radius 5cm and height 15cm. For surface area: 2 × π × 5 × 15 + 2 × π × 5² = 628cm². For volume of a water tank with radius 25cm and height 120cm: π × 25² × 120 = 235,500cm³.
Quick tip: Remember that volume always uses cubic units (cm³) whilst surface area uses square units (cm²).
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Spheres
A sphere is perfectly round like a football or tennis ball. Unlike other 3D shapes, spheres only need the radius to calculate everything - no height or width measurements required.
The volume formula is (4/3)πr³. For a ball with radius 7cm, you'd get (4/3) × π × 7³ = 436.75cm³. That's quite a lot of space inside!
Surface area uses 4πr². If your sphere has a radius of 10cm, the calculation becomes 4π × 10² = 502.4cm². This formula is much simpler than cylinders because there's only one curved surface to worry about.
Remember: Spheres are the only 3D shape where you don't need to think about separate faces - it's all one smooth surface.
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Pyramids
Pyramids have a flat base (usually square) with triangular faces that meet at a point at the top. Think of the Egyptian pyramids, but smaller and with precise measurements!
The volume formula is (length × width × height) ÷ 3. For a pyramid that's 8cm by 6cm at the base and 9cm tall, you'd calculate: (8 × 6 × 9) ÷ 3 = 144cm³. Notice how it's one-third of what a rectangular box would be.
Surface area means adding up all the faces. You need the area of the square base plus all four triangular sides. For a pyramid with base 5cm × 5cm and triangular faces of 20cm² each: base area = 25cm², four triangular faces = 80cm², total = 105cm².
Pro tip: Always remember to divide by 3 for pyramid volume - it's the most common mistake students make!
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Cones
A cone looks like an ice cream cone or traffic cone - it has a circular base that tapers to a point. You'll need to know the radius of the base and either the height or slant height.
The volume formula is (1/3)πr²h, where h is the perpendicular height (straight up from base to tip). For a cone with radius 5cm and height 8cm: (1/3) × π × 5² × 8 = 209.3cm³.
Surface area combines the circular base (πr²) with the curved surface (πrl, where l is the slant height). With radius 14cm and slant height 8cm, you'd calculate: π × 14² + π × 14 × 8 = 508cm².
Key point: Make sure you know whether you're given the perpendicular height or slant height - they're different measurements!
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?
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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.
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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
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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
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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
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Elisha
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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
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