This study notes covers Worked Example: Cuboid Diagonal 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 4 of 5 in this topic. Use this study notes to connect the idea to the wider topic before moving on to questions and flashcards.
Worked Example: Cuboid Diagonal
Find the space diagonal of a cuboid 3cm × 4cm × 12cm.
Method 1: Two steps
Base diagonal: √(3² + 4²) = √25 = 5
Space diagonal: √(5² + 12²) = √(25 + 144) = √169 = 13 cm
Method 2: Direct
d² = 3² + 4² + 12² = 9 + 16 + 144 = 169
d = √169 = 13 cm
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.