Ever wondered how to work out the space inside a...
Maths197 views·Updated 11 Aug 2026·4 pagesVolume and Surface Area Calculations
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Circle Areas and Cylinder Volumes
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!
2
of 4
Hollow Cylinders and Cones
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!
3
of 4
Sphere Volume and Cylinder Surface Area
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!
4
of 4
Surface Area Formula Breakdown
For cylinder surface area, you need two key measurements: circumference (C = diameter × π) 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!
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Maths197 views·Updated 11 Aug 2026·4 pagesVolume and Surface Area Calculations
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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...
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Circle Areas and Cylinder Volumes
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!
2
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Hollow Cylinders and Cones
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!
3
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Sphere Volume and Cylinder Surface Area
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!
4
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Surface Area Formula Breakdown
For cylinder surface area, you need two key measurements: circumference (C = diameter × π) 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!
We thought you’d never ask...
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.
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Students love us — and so will you.
4.6/5App Store
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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.
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Samantha KlichAndroid 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.
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