Geometry & MeasuresTopic Summary
Knowledge Organiser: Volume & Surface Area of Spheres
Part of Volume & Surface Area of Spheres · GCSE GCSE Mathematics revision
This topic summary covers Knowledge Organiser: Volume & Surface Area of Spheres within Volume & Surface Area of Spheres for GCSE Mathematics. Revise Volume & Surface Area of Spheres in Geometry & Measures for GCSE Mathematics with 12 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 4 of 4 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 4 of 4
Practice
12 questions
Recall
3 flashcards
Knowledge Organiser: Volume & Surface Area of Spheres
Key Terms
- Sphere: A perfectly round 3D shape — every point on the surface is the same distance from the centre
- Hemisphere: Exactly half a sphere
- Radius (r): Distance from centre to surface
Must-Know Facts
- Both sphere formulas are GIVEN in GCSE exams — know how to use them
- Hemisphere volume = ½ × (4/3)πr³ = (2/3)πr³
- Hemisphere total surface area = curved half + flat circle = 2πr² + πr² = 3πr²
- Volume grows with r³ — doubling radius multiplies volume by 8
- Surface area grows with r² — doubling radius multiplies SA by 4
Key Formulas
- Sphere volume: V = (4/3)πr³
- Sphere surface area: SA = 4πr²
- Hemisphere volume: V = (2/3)πr³
- Hemisphere total SA: SA = 3πr²
Common Mistakes
- Using diameter instead of radius: Both sphere formulas use r — if given d, halve it first
- Hemisphere surface area: Total SA = 2πr² (curved) + πr² (flat circle) = 3πr² — don't forget the flat face
- Volume formula: V = (4/3)πr³ — the power is 3, not 2
- Exact answers: Leave as e.g. 36π cm³ when asked for exact answers in terms of π