Key Terms
- Surface area: Total area of all faces of a 3D shape — in square units
- Net: A 3D shape unfolded flat — helps identify all faces
- Curved surface area: The area of the curved face (cylinder, cone)
- Slant height (l): The sloped length of a cone's side; l = √(r² + h²)
Must-Know Facts
- Surface area is ALWAYS in square units: cm², m²
- Cylinder: two circular ends + one rectangle wrapped round
- Cone total SA = base circle + curved surface = πr² + πrl
- Draw the net to make sure you count ALL faces
- Prism SA = 2 × cross-section area + perimeter × length
Key Formulas
- Cuboid: SA = 2(lw + lh + wh)
- Cube: SA = 6s²
- Cylinder: SA = 2πr² + 2πrh
- Cone: SA = πr² + πrl
- Sphere: SA = 4πr²
Common Mistakes
- Forgetting all faces: Count every face — a cuboid has 6 faces in 3 pairs; draw a net to check
- Cylinder — missing a circular face: Total SA = 2πrh + 2πr² — both circular ends plus the curved surface
- Cone — using vertical height: Curved SA uses slant height l, not vertical height h
- Units: Surface area is always in square units (cm², m²) — not cubic units
This topic summary covers Knowledge Organiser: Surface Area within Surface Area for GCSE Mathematics. Revise Surface Area 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 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.
Practice questions for Surface Area
A cuboid has length l, width w and height h. What is its total surface area?
Explain how you could use a net to find the surface area of a 3D solid.
Quick recall flashcards
Net
Unfolded 3D shape showing all faces
Surface Area
Sum of areas of all faces