Knowledge Organiser: Volume of Pyramids & Cones
Key Terms
- Pyramid: 3D shape with a polygon base tapering to a point (apex)
- Cone: A solid like a pyramid, but 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
- Cone and pyramid volume formulas are given in the exam question when you need them, and the prism formula is on your formula sheet
- 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
Worked Examples
Find the volume of a cone with radius 3cm and height 7cm. Solution V = (1/3) × πr²h V = (1/3) × π × 3² × 7 V = (1/3) × π × 9 × 7 = 21π = 65.97 cm³ (2 d.p.)