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Geometry & MeasuresKey Facts

Key Facts

Part of Pythagoras in 3D — GCSE Mathematics

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. This topic appears less often, but it can still be a useful differentiator on mixed-topic papers. It is section 2 of 4 in this topic. Use this key facts to connect the idea to the wider topic before moving on to questions and flashcards.

Topic position

Section 2 of 4

Practice

12 questions

Recall

2 flashcards

Key Facts

3D Formulad² = x² + y² + z² (space diagonal)
MethodApply Pythagoras twice - first on base, then using result
Common shapesCuboid diagonals, pyramid heights, cone slant heights

Keep building this topic

Read this section alongside the surrounding pages in Pythagoras in 3D. That gives you the full topic sequence instead of a single isolated revision point.

From Flat to 3DMethod: 3D PythagorasWorked Example: Cuboid Diagonal

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?

  • A. d = l + w + h
  • B. d² = l² + w²
  • C. d² = l² + w² + h²
  • D. d = √(l + w + h)
1 markfoundation

Describe the two-step method for finding the space diagonal of a cuboid with dimensions l, w, and h.

2 marksstandard

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.

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From Flat to 3D

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Method: 3D Pythagoras