Ratio of areas from a ratio of radii — Aptitude Question
Ratio of areas from a ratio of radii: The radii of two circles are in the ratio 2 : 3. What is the ratio of their… Answer and worked solution on CodeKairo.
- Topic: Ratio & Proportion
- Section: Quantitative Aptitude
- Difficulty: Easy
- Time target: 40 seconds
Question
The radii of two circles are in the ratio 2 : 3. What is the ratio of their areas?
Options
- 2 : 3
- 4 : 9
- 8 : 27
- 16 : 81
Show the answer and the worked solution
Correct answer: B. 4 : 9
Worked solution
- Area ∝ r², so the ratio of areas = 2² : 3² = 4 : 9.
Answer: 4 : 9.
The idea
Lengths in ratio a : b give areas a² : b² and volumes a³ : b³. Knowing all three saves time whenever a question scales a figure.
Shortcut. Plug r = 2 and r = 3 into πr²: 4π and 9π, so 4 : 9.
Common trap. "2 : 3" — keeping the radius ratio and forgetting that area depends on the square of the radius.