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