Area & Volume — GCSE Mathematics Revision
Revise Area & Volume for GCSE Mathematics. Step-by-step explanation, worked examples, common mistakes and exam-style practice aligned to AQA, Edexcel and OCR.
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Go to Surface Area of 3D ShapesWhat is Area & Volume?
Area measures the space inside a 2D shape (in square units). Volume measures the space inside a 3D shape (in cubic units). You need to know formulae for rectangles, triangles, parallelograms, trapeziums, circles, prisms, cylinders, cones, spheres and pyramids. For prisms, volume = cross-section area × length. Many exam questions combine shapes or require you to work backwards from a given volume.
Step-by-step explanationWorked example
Find the volume of a cylinder with radius 4 cm and height 10 cm. V = πr²h = π × 4² × 10 = π × 160 = 502.7 cm³ (1 d.p.).
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Common mistakes
- 1Using diameter instead of radius in circle formulae (A = πr², not πd²).
- 2Forgetting to halve the height in the triangle area formula: A = ½ × base × height.
- 3Mixing up surface area and volume — read the question carefully.
- 4Not converting units consistently (e.g. mixing cm and m in the same calculation).
Area & Volume exam questions
Exam-style questions for Area & Volume with mark-scheme style solutions and timing practice. Aligned to AQA, Edexcel and OCR specifications.
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Step-by-step method
Step-by-step explanation
4 steps · Worked method for Area & Volume
Core concept
Area measures the space inside a 2D shape (in square units). Volume measures the space inside a 3D shape (in cubic units). You need to know formulae for rectangles, triangles, parallelograms, trapeziu…
Frequently asked questions
Do I need to memorise all the volume formulae?
You should memorise formulae for prisms, cylinders, and cuboids. Formulae for cones (⅓πr²h), spheres (⁴⁄₃πr³), and pyramids (⅓ × base area × height) are given on the formula sheet for most boards.
How do I find the volume of a composite shape?
Break the shape into simpler shapes you know the formulae for, calculate each volume separately, then add (or subtract for holes) them together.