A circle inside a square — Mensuration Aptitude Question
A circle inside a square: A circle is inscribed in a square of side 14 cm. What is the area of the circle? Answer and worked solution on CodeKairo.
- Topic: Mensuration
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 75 seconds
Question
A circle is inscribed in a square of side 14 cm. What is the area of the circle? (Take π = 22/7.)
Options
- 154 cm²
- 196 cm²
- 308 cm²
- 616 cm²
Show the answer and the worked solution
Correct answer: A. 154 cm²
Worked solution
- The inscribed circle has diameter 14 cm, so radius 7 cm.
- Area = (22/7) × 49 = 154 cm².
Answer: 154 cm².
The idea
For an inscribed circle the diameter matches the side; for a circumscribed circle the diameter matches the diagonal. Deciding which applies comes first.
Shortcut. An inscribed circle fills π/4 of its square: 196 × 11/14 = 154 cm².
Common trap. "616 cm²" — using the side 14 as the radius; the side is the diameter, so the radius is 7.