Volume of a cube from its surface area — Aptitude Question
Volume of a cube from its surface area: The total surface area of a cube is 216 cm². What is its volume? Answer and worked solution on CodeKairo.
- Topic: Mensuration
- Section: Quantitative Aptitude
- Difficulty: Easy
- Time target: 40 seconds
Question
The total surface area of a cube is 216 cm². What is its volume?
Options
- 144 cm³
- 196 cm³
- 216 cm³
- 256 cm³
Show the answer and the worked solution
Correct answer: C. 216 cm³
Worked solution
- 6a² = 216 → a² = 36 → a = 6 cm.
- Volume = 6³ = 216 cm³.
Answer: 216 cm³.
The idea
Cube: surface 6a², volume a³, diagonal a√3. The coincidence that 216 appears twice here is because a = 6 makes 6a² = a³.
Shortcut. A cube's volume must be a perfect cube: of the options only 216 = 6³ is one (144, 196 and 256 are squares, not cubes).
Common trap. 144 cm³ — distrusting an answer equal to the given 216 and reaching for another option; 144 is not even a cube, and a = 6 really makes 6a² and a³ both 216.