Geometry & MeasuresTopic Summary

Knowledge Organiser: Volume of Pyramids & Cones

Part of Volume of Pyramids & Cones · GCSE GCSE Mathematics revision

This topic summary covers Knowledge Organiser: Volume of Pyramids & Cones within Volume of Pyramids & Cones for GCSE Mathematics. Revise Volume of Pyramids & Cones in Geometry & Measures for GCSE Mathematics with 10 exam-style questions and 3 flashcards. This topic appears regularly enough that it should still be part of a steady revision cycle. It is section 5 of 5 in this topic. Use this topic summary to connect the idea to the wider topic before moving on to questions and flashcards.

Topic position

Section 5 of 5

Practice

10 questions

Recall

3 flashcards

Knowledge Organiser: Volume of Pyramids & Cones

Key Terms
  • Pyramid: 3D shape with a polygon base tapering to a point (apex)
  • Cone: A pyramid with a circular base
  • Apex: The pointed top of a pyramid or cone
  • Perpendicular height: The vertical height straight up from the base to apex
  • Slant height: The distance along the sloped face (NOT used in volume)
Must-Know Facts
  • Both pyramid and cone volume = ⅓ × base area × height
  • Both hold exactly ⅓ of the matching prism/cylinder volume
  • Always use PERPENDICULAR height, never slant height
  • Sphere, cone, cylinder formulas are given in GCSE exams — you must use them correctly
  • Volume in cubic units: cm³, m³
Key Formulas
  • Pyramid: V = ⅓ × base area × h
  • Cone: V = ⅓ × πr² × h
  • Cone curved surface area: A = πrl (l = slant height)
  • Slant height: l = √(r² + h²)
Common Mistakes
  • Forgetting the ⅓: Pyramids and cones have volume = ⅓ × base area × h — always include the ⅓
  • Slant height vs vertical height: V uses vertical height h; curved surface area uses slant height l = √(r² + h²)
  • Cone surface area: Total SA = πr² (base) + πrl (curved part) — don't forget the base
  • Units: Volume in cm³; surface area in cm² — always write the correct units

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Practice Questions for Volume of Pyramids & Cones

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

  • A. πr²h
  • B. (1/3)πr²h
  • C. (1/2)πr²h
  • D. (2/3)πr³
1 markfoundation

Explain why the volume of a cone is one third of the volume of a cylinder with the same base and height.

2 markshigher

Quick Recall Flashcards

The 1/3 Rule
Pyramids and cones are both 1/3 of their matching prism/cylinder. V = (1/3) × base area × height
Volume of Cone
⅓ × πr² × h

10 questions on Volume of Pyramids & Cones — practise free

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