Multiple choice

The curved surface areas of two spheres are in the ratio of 1 : 4. Find the ratio of their volumes.

  1. 1 : 4

  2. 1 : 8

  3. 1 : 10

  4. 1 : 5

  5. 1 : 6
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B Correct answer
Explanation

The ratio of surface areas of two spheres is r1^2/r2^2 = 1/4, so the ratio of radii r1/r2 = 1/2. The ratio of volumes is (r1/r2)^3 = (1/2)^3 = 1/8.

AI explanation

Because the curved surface area of a sphere is 4 * pi * r^2, a surface area ratio of 1 : 4 means the ratio of their radii is 1 : 2. Since the volume of a sphere is 4/3 * pi * r^3, the ratio of their volumes is the cube of the radii ratio. Therefore, the volume ratio is 1^3 : 2^3, which is 1 : 8.

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