Multiple choice

The radius of a spherical balloon increases from $7cm$ to $14cm$ as air is being pumped into it. Find the ratio of volumes of the balloon in the two cases.

  1. $1:8$
  2. $1:9$
  3. $5:8$

  4. None of these
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A Correct answer
Explanation

Volume of sphere = (4/3) * pi * r^3. Ratio of volumes = (r1/r2)^3 = (7/14)^3 = (1/2)^3 = 1/8.

AI explanation

The volume of a sphere is calculated as (4/3)πr^3, so the ratio of the volumes of the balloon in the two cases is the cube of the ratio of their radii. Given the radii are 7 cm and 14 cm, their ratio is 1:2. The ratio of their volumes is 1^3 : 2^3, which equals 1:8. The ratio is 1:8.

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