Volume from the surface area — Mensuration Aptitude Question
Volume from the surface area: The total surface area of a cube is 150 cm². What is its volume? Answer and worked solution on CodeKairo.
- Topic: Mensuration
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 60 seconds
Question
The total surface area of a cube is 150 cm². What is its volume?
Options
- 100 cm³
- 125 cm³
- 150 cm³
- 216 cm³
Show the answer and the worked solution
Correct answer: B. 125 cm³
Worked solution
- 6a² = 150 → a² = 25 → a = 5 cm.
- Volume = 5³ = 125 cm³.
Answer: 125 cm³.
The idea
Route through the edge length. Surface area gives a, and a gives volume and diagonal alike.
Shortcut. One face is 150 ÷ 6 = 25 cm², and volume = face area × √(face area) = 25 × 5 = 125 cm³.
Common trap. "216 cm³" — taking the edge as 6 (the number of faces) instead of √(150 ÷ 6) = 5.