Multiple choice

The radius of a sphere is increased by 140%. By what percent will its volume increase?

  1. 174.4%

  2. 1,382.4%

  3. 274.4%

  4. 1,282.4%
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

If radius r increases by 140%, the new radius is r + 1.4r = 2.4r. The volume of a sphere is proportional to r^3. The new volume is (2.4)^3 = 13.824 times the original volume. The increase is 13.824 - 1 = 12.824, which is 1,282.4%.

AI explanation

A 140% increase means the new radius is 2.4 times the original radius. Since volume is proportional to the cube of the radius, the new volume is 2.4 cubed times the original, which equals 13.824 times the original. This represents a 1282.4% increase over the original volume.

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