Multiple choice

Radii of two solid hemispheres are in the ratio $3:5$. Find the ratio of their curved surface areas.

  1. ${C}_{1}:{C}_{2}=9:25$
  2. ${C}_{1}:{C}_{2}=2:25$
  3. ${C}_{1}:{C}_{2}=9:5$

  4. None of these
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A Correct answer
Explanation

The curved surface area of a hemisphere is 2*pi*r^2. The ratio of areas is the square of the ratio of radii. Since the radii are in ratio 3:5, the areas are in ratio 3^2:5^2, which is 9:25.

AI explanation

The curved surface area of a hemisphere is 2πr^2, so the ratio of their curved surface areas is the square of the ratio of their radii. Given the radii ratio is 3:5, the area ratio is 3^2 : 5^2. This makes the ratio of their curved surface areas 9:25.

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