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HomeAQA GCSE MathematicsVolume and surface area of prisms, cylinders, pyramids, cones and spheres
AQA · GCSE · Mathematics

Volume and surface area of prisms, cylinders, pyramids, cones and spheres
Practice Questions

20 AQA GCSE Mathematics questions on Volume and surface area of prisms, cylinders, pyramids, cones and spheres, each with instant feedback and a full examiner-style mark scheme.

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✨ Revision guide includes key terms, worked examples and exam technique for Volume and surface area of prisms, cylinders, pyramids, cones and spheres.

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Question 1 · 1 mark · Difficulty 1/3

What is the formula for the volume of a cylinder with radius r and height h?

  1. V = πr²h
  2. V = 2πrh
  3. V = πrh²
  4. V = πr²h²
Show answer & explanation
✓ Answer: AV = πr²h
The volume of a cylinder is found by multiplying the area of the circular cross-section (πr²) by the height h. Common errors include confusing this with the curved surface area formula 2πrh.
Question 2 · 1 mark · Difficulty 2/3

The volume of a cone is 150π cm³ and its radius is 5 cm. What is the perpendicular height of the cone?

  1. 18 cm
  2. 6 cm
  3. 9 cm
  4. 54 cm
Show answer & explanation
✓ Answer: A18 cm
Using V = (1/3)πr²h: 150π = (1/3)π × 25 × h, so 150 = (25h)/3, giving h = 450/25 = 18 cm. A common error is forgetting the 1/3, which would give h = 6 cm instead.
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AQA GCSE Mathematics: Volume and surface area of prisms, cylinders, pyramids, cones and spheres FAQ

How many AQA GCSE Mathematics questions on Volume and surface area of prisms, cylinders, pyramids, cones and spheres are there on Kramizo?
Kramizo currently has 20 exam-board-aligned practice questions on Volume and surface area of prisms, cylinders, pyramids, cones and spheres for AQA GCSE Mathematics, with new questions added every week. Each question gives you instant feedback and a full examiner-style mark scheme that tells you exactly what would earn marks on a real AQA paper. The questions span the full difficulty range — from straightforward recall (level 1) right up to multi-step reasoning and evaluation (level 3) — so the bank works for first-pass revision and final exam-week stress testing alike.
Is Kramizo free for AQA GCSE students preparing for Mathematics?
Yes — completely free. Every student gets 45 questions a day on the free plan, with no card required and no trial countdown. That free quota works across every subject and every topic in our bank, so you can mix Volume and surface area of prisms, cylinders, pyramids, cones and spheres practice with other Mathematics topics or even switch to a totally different AQA subject without paying anything. Kramizo's optional Pro plan removes the daily cap and adds detailed progress analytics, but the free tier is the real product — used by thousands of GCSE, IGCSE and CSEC students.
Are the Volume and surface area of prisms, cylinders, pyramids, cones and spheres questions aligned to the official AQA GCSE Mathematics syllabus?
Every question is written against the published AQA GCSE Mathematics specification, including the exact command words (state, describe, explain, calculate, evaluate, etc.), mark allocations, and difficulty tier you'd see on a real AQA paper. Explanations are written in the style of official examiner mark schemes — they tell you what is being awarded marks and why distractors are wrong, not just whether you got it right. The bank is continually refined to match the latest syllabus updates from AQA.
How is Volume and surface area of prisms, cylinders, pyramids, cones and spheres typically tested on AQA GCSE Mathematics papers?
Volume and surface area of prisms, cylinders, pyramids, cones and spheres appears across multiple question types on real AQA GCSE Mathematics papers — most commonly as multiple-choice questions in the objective section, structured short-answer questions in the main paper, and occasionally as part of an extended response. Kramizo's practice bank reflects that mix: 4-option MCQs, true/false statements, fill-in-the-blank key terms, multi-select questions, and ordering questions. Working through the bank gives you exposure to every question style examiners actually use.

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