Multiple choice

The ratio of the total surface areas of two solid hemisphere is 25 : 16 then ratio of their volumes will be

  1. $5:4$
  2. $125:64$
  3. $27:16$
  4. $81:64$
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B Correct answer
Explanation

Ratio of surface areas of two hemispheres = (r1^2 / r2^2) = 25/16, so r1/r2 = 5/4. Ratio of volumes = (r1^3 / r2^3) = (5/4)^3 = 125/64.

AI explanation

The surface area of a solid hemisphere is 3 times pi times r squared, so the ratio of the radii is the square root of (25 divided by 16), which is 5 to 4. The volume of a solid hemisphere is two thirds times pi times r cubed, so the ratio of the volumes is 5 cubed to 4 cubed. This gives the ratio 125 to 64.

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