A cuboid has dimensions 3cm × 4cm × 5cm. Find the length of the space diagonal.
Step 1 Find the base diagonal first
Base diagonal² = 3² + 4² = 9 + 16 = 25
Base diagonal = 5 cm
Step 2 Use base diagonal and height for space diagonal
Space diagonal² = 5² + 5² = 25 + 25 = 50
Space diagonal = √50 = 5√2 ≈ 7.07 cm
This study notes covers Worked Example: Space Diagonal of a Cuboid within 3D Trigonometry for GCSE Mathematics. Revise 3D Trigonometry 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 6 in this topic. Use this study notes to connect the idea to the wider topic before moving on to questions and flashcards.
Practice questions for 3D Trigonometry
To find the angle between a line and a horizontal plane in a 3D problem, which technique is typically used?
Describe the general method for finding the angle between a line and a plane in a 3D problem.