Diagonal of a cube — Mensuration Aptitude Question
Diagonal of a cube: What is the length of the diagonal of a cube of side 6 cm? (Take √3 = 1.73.) Answer and worked solution on CodeKairo.
- Topic: Mensuration
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 50 seconds
Question
What is the length of the diagonal of a cube of side 6 cm? (Take √3 = 1.73.)
Options
- 6√2 cm
- 6√3 cm
- 12 cm
- 18 cm
Show the answer and the worked solution
Correct answer: B. 6√3 cm
Worked solution
- Diagonal = a√3 = 6√3 cm (about 10.39 cm).
Answer: 6√3 cm.
The idea
A cube's face diagonal is a√2 and its space diagonal a√3. The question asks for the longer of the two.
Shortcut. Space diagonal² = 3a² = 108, so the diagonal is √108 = 6√3 ≈ 10.4 cm — longer than a face diagonal (≈ 8.5) but shorter than 12.
Common trap. 6√2 cm — the diagonal of one face; the question asks for the diagonal through the cube.