Multiple choice

DIRECTIONS : Select the correct alterative from the given choices. Find the percentage increase in the volume of a sphere, if its radius increases by 200%.

  1. 700%

  2. 800%

  3. 2600%

  4. 2700%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

If the radius increases by 200%, the new radius is r + 2r = 3r. The volume of a sphere is proportional to the cube of the radius, so the new volume is (3r)^3 = 27r^3. The increase is 27r^3 - r^3 = 26r^3, which is 2600% of the original volume.

AI explanation

Using the volume of a sphere formula, volume is proportional to the cube of its radius. If the radius increases by 200%, the new radius is 3 times the original, making the new volume 3 cubed, or 27 times the original volume. The increase in volume is 27 minus 1, giving 26, which when multiplied by 100 equals a 2600% increase.

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