Geometry & MeasuresStudy Notes

Worked Example: Space Diagonal of a Cuboid

Part of 3D Trigonometry — GCSE Mathematics

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. This topic appears less often, but it can still be a useful differentiator on mixed-topic papers. 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.

Topic position

Section 4 of 5

Practice

12 questions

Recall

2 flashcards

Worked Example: Space Diagonal of a Cuboid

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

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?

A. Calculate the 3D distance directly using one formula
B. Identify a right-angled triangle and apply SOHCAHTOA
C. Use the cosine rule only
D. Use the sine rule with the bearing angle

1 markfoundation

Describe the general method for finding the angle between a line and a plane in a 3D problem.

3 marksstandard

Worked Example: Space Diagonal of a Cuboid

Worked Example: Space Diagonal of a Cuboid

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Practice Questions for 3D Trigonometry

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