Area of a quadrant — Mensuration Aptitude Question
Area of a quadrant: What is the area of a quadrant of a circle of radius 14 cm? (Take π = 22/7.) Answer and worked solution on CodeKairo.
- Topic: Mensuration
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 60 seconds
Question
What is the area of a quadrant of a circle of radius 14 cm? (Take π = 22/7.)
Options
- 77 cm²
- 154 cm²
- 308 cm²
- 616 cm²
Show the answer and the worked solution
Correct answer: B. 154 cm²
Worked solution
- Full circle area = (22/7) × 14² = 616 cm².
- A quadrant is one quarter: 616 ÷ 4 = 154 cm².
Answer: 154 cm².
The idea
A sector of angle θ has area (θ/360) × πr². A quadrant is 90°, so exactly a quarter.
Shortcut. A quarter of πr²: (22/7) × 14 × 14 ÷ 4 = 22 × 7 = 154 cm² once the 7 and the 4 cancel.
Common trap. "616 cm²" — stopping at the full circle's area and forgetting to take one quarter for the quadrant.