Doubling the radius — Mensuration Aptitude Question
Doubling the radius: If the radius of a circle is doubled, by what factor does its area increase? Answer and worked solution on CodeKairo.
- Topic: Mensuration
- Section: Quantitative Aptitude
- Difficulty: Easy
- Time target: 40 seconds
Question
If the radius of a circle is doubled, by what factor does its area increase?
Options
- 2
- 3
- 4
- 8
Show the answer and the worked solution
Correct answer: C. 4
Worked solution
- Area ∝ r², so doubling r multiplies the area by 2² = 4.
Answer: 4.
The idea
Lengths scale by k, areas by k², volumes by k³. Doubling the radius would multiply the circumference by only 2.
Shortcut. Try r = 1 and r = 2: the areas are π and 4π, a factor of 4.
Common trap. "2" — assuming area grows in step with the radius; that is true of the circumference, not the area.