Geometry & MeasuresDeep Dive

Method: 3D Pythagoras

Part of Pythagoras in 3D · GCSE GCSE Mathematics revision

This deep dive covers Method: 3D Pythagoras 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 3 of 5 in this topic. Use this deep dive to connect the idea to the wider topic before moving on to questions and flashcards.

Topic position

Section 3 of 5

Practice

12 questions

Recall

2 flashcards

Method: 3D Pythagoras

1 Identify the right-angled triangles in the 3D shape

2 First Pythagoras: find the base diagonal

3 Second Pythagoras: use base diagonal + height

4 Or use the direct formula: d² = x² + y² + z²

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.

Key Facts Worked Example: Cuboid Diagonal From Flat to 3D Knowledge Organiser: Pythagoras in 3D

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

d² = x² + y² + z² for space diagonal. Or use 2D Pythagoras twice: first on base, then with height.

3D Pythagoras

Use Pythagoras twice: once for base diagonal, once for 3D diagonal

12 questions on Pythagoras in 3D — practise free

Instant marking, adaptive difficulty, and 2 spaced repetition flashcards. Free until your GCSEs.

Try PrepWise Free

Key Facts

Worked Example: Cuboid Diagonal