A wire bent into a square — Mensuration Aptitude Question
A wire bent into a square: A wire in the shape of a circle of radius 28 cm is bent into a square. Answer and worked solution on CodeKairo.
- Topic: Mensuration
- Section: Quantitative Aptitude
- Difficulty: Hard
- Time target: 105 seconds
Question
A wire in the shape of a circle of radius 28 cm is bent into a square. What is the area of the square? (Take π = 22/7.)
Options
- 1,936 cm²
- 2,916 cm²
- 3,136 cm²
- 3,844 cm²
Show the answer and the worked solution
Correct answer: A. 1,936 cm²
Worked solution
- Circumference = 2 × (22/7) × 28 = 176 cm.
- As a square's perimeter, each side = 176 ÷ 4 = 44 cm.
- Area = 44² = 1,936 cm².
Answer: 1,936 cm².
The idea
Bending a wire preserves its length, so circumference becomes perimeter. The shape changes but the total length does not.
Shortcut. The side is a quarter of 2πr, i.e. πr/2 = (22/7 × 28) ÷ 2 = 44, and 44² = 1,936.
Common trap. 3,136 cm² — taking the square's side as the circle's diameter (56 cm); the wire's 176 cm length gives a 44 cm side.