Volume of a sphere — Mensuration Aptitude Question
Volume of a sphere: What is the volume of a sphere of radius 3 cm? (Take π = 22/7.) Answer and worked solution on CodeKairo.
- Topic: Mensuration
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 75 seconds
Question
What is the volume of a sphere of radius 3 cm? (Take π = 22/7.)
Options
- 88.6 cm³
- 113.1 cm³
- 121.5 cm³
- 132 cm³
Show the answer and the worked solution
Correct answer: B. 113.1 cm³
Worked solution
- Volume = (4/3) × (22/7) × 27 = (4 × 22 × 27)/(3 × 7) = 2376/21 ≈ 113.1 cm³.
Answer: 113.1 cm³.
The idea
Sphere: volume (4/3)πr³ and surface 4πr². Cancel the 3 against the 27 before multiplying to keep the numbers small.
Shortcut. (4/3)π × 27 = 36π, and 36π lies between 36 × 3.1 = 111.6 and 36 × 3.2 = 115.2 — only 113.1 fits.
Common trap. 132 cm³ — slipping 792 ÷ 7 to 792 ÷ 6 when finishing 36 × 22/7; dividing by 7 gives 113.1.