This key facts covers Key Facts within Pythagoras in 3D for GCSE Mathematics. Revise Pythagoras in 3D in Geometry & Measures for GCSE Mathematics with 12 exam-style questions and 2 flashcards. Use this page as part of a wider topic revision path rather than treating it as an isolated fact. It is section 2 of 5 in this topic. Use this key facts to connect the idea to the wider topic before moving on to questions and flashcards.
Key Facts
| 3D Formula | d² = x² + y² + z² (space diagonal) |
| Method | Apply Pythagoras twice - first on base, then using result |
| Common shapes | Cuboid diagonals, pyramid heights, cone slant heights |
Practice questions for Pythagoras in 3D
A cuboid has length l, width w, and height h. Which formula gives the length of the space diagonal d?
Describe the two-step method for finding the space diagonal of a cuboid with dimensions l, w, and h.
Quick recall flashcards
3D Pythagoras
Use Pythagoras twice: once for base diagonal, once for 3D diagonal
3D Pythagoras
d² = x² + y² + z² for space diagonal. Or use 2D Pythagoras twice: first on base, then with height.