Multiple choice

If the radius of the sphere is increased by $100\%$, the volume of the corresponding sphere is increased by-

  1. $200\%$
  2. $500\%$
  3. $700\%$
  4. $800\%$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Volume of a sphere is proportional to r^3. If radius increases by 100%, the new radius is 2r. The new volume is proportional to (2r)^3 = 8r^3. The increase is (8r^3 - r^3) / r^3 = 7, which is 700%.

AI explanation

Let the original radius be r, so the original volume of the sphere is (4/3)πr^3. A 100 percent increase means the new radius is 2r, making the new volume (4/3)π(2r)^3 = (4/3)π(8r^3) = 8 times the original volume. The increase in volume is 8 - 1 = 7 times the original volume, which equals an increase of 700 percent.

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