Multiple choice

The capacities of two hemispherical bowl are 25.6 litre and 86.5 litre respectively. what is ratio of the internal curved surface area?

  1. 2 : 3

  2. 3 : 5

  3. 4 : 5

  4. 4 : 9
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For hemispheres, the ratio of curved surface areas is (4πr²/2) : (4πR²/2) = r² : R². Since volume of hemisphere = (2/3)πr³, the radii are proportional to the cube roots of volumes. r ∝ ³√25.6 ≈ 2.96, R ∝ ³√86.5 ≈ 4.42. Therefore, r² : R² = (2.96)² : (4.42)² = 8.76 : 19.54 ≈ 4:9. The key insight is that surface area ratio is the square of the cube root ratio of volumes.

Keep practicing — related questions