Multiple choice

If the radius of a sphere is doubled what is the ratio of the volume of the first sphere to that of the second?

  1. 2:8

  2. 1:2

  3. 1:3

  4. 1:8
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Explanation

Volume of a sphere is proportional to the cube of its radius. If the radius is doubled (2r), the volume becomes (2r)^3 = 8r^3. The ratio is 1:8.

AI explanation

The volume of a sphere is directly proportional to the cube of its radius, given by the formula (4/3)pi*r^3. When the radius is doubled, the new volume becomes (4/3)*pi(2r)^3, which simplifies to 8 times the original volume. Therefore, the ratio of the original volume to the new volume is 1:8. The result is 1:8.

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