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AQASpec G16-G17Foundation & Higher~30 min

Volume & Surface Area

Mathematics · Topic revision workspace

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Read the notes, score 80% and know 75% of the cards.

Topic overview

What you need to know

Volume & Surface Area is a key part of GCSE Mathematics. Build fluency with the method, then apply it to unfamiliar and multi-step problems. Volume = length × width × height. Volume = area of cross-section × length. Works for any prism shape. Volume = πr²h, where r is the radius of the base and h is the height.

Exam tip

Write every stage of your method. Method marks can still be earned when the final answer is wrong.

Revision notes

Core ideas

Secure these ideas first. Say each definition in your own words, then connect it to the topic overview.

  • Volume of a Cuboid: Volume = length × width × height.
  • Volume of a Prism: Volume = area of cross-section × length. Works for any prism shape.
  • Volume of a Cylinder: Volume = πr²h, where r is the radius of the base and h is the height.
  • Volume of a Cone: Volume = ⅓πr²h. It's one third of the volume of a cylinder with the same base and height.

Revision notes

Apply it in the exam

The exam will rarely ask for an isolated definition. Practise selecting the right idea and using it as part of a complete explanation or method.

  • Volume of a Sphere: Volume = (4/3)πr³.
  • Surface Area of a Cuboid: SA = 2(lw + lh + wh). Add up the area of all six faces.
  • Surface Area of a Cylinder: SA = 2πr² + 2πrh. Two circular ends plus the curved surface.
  • Surface Area of a Sphere: SA = 4πr².

Core knowledge

Key facts for Volume & Surface Area

1

Volume of a Cuboid

Volume = length × width × height.

2

Volume of a Prism

Volume = area of cross-section × length. Works for any prism shape.

3

Volume of a Cylinder

Volume = πr²h, where r is the radius of the base and h is the height.

4

Volume of a Cone

Volume = ⅓πr²h. It's one third of the volume of a cylinder with the same base and height.

5

Volume of a Sphere

Volume = (4/3)πr³.

6

Surface Area of a Cuboid

SA = 2(lw + lh + wh). Add up the area of all six faces.

7

Surface Area of a Cylinder

SA = 2πr² + 2πrh. Two circular ends plus the curved surface.

8

Surface Area of a Sphere

SA = 4πr².

Active recall

Close the notes and answer these

  1. 1.Without looking, explain volume of a cuboid and give one example or consequence.
  2. 2.Without looking, explain volume of a prism and give one example or consequence.
  3. 3.Without looking, explain volume of a cylinder and give one example or consequence.
  4. 4.Without looking, explain volume of a cone and give one example or consequence.

Content reviewed 23 July 2026 against the current linked specification.

Finished learning?

Mark the notes complete, then test what you can recall.

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