Multiple choice

Each of the height and radius of the base of a right circular cone is increased by $100$%. The volume of the cone will be increased by

  1. $700$%
  2. $500$%
  3. $300$%
  4. $100$%
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A Correct answer
Explanation

New radius R = 2r, new height H = 2h. New volume = (1/3) * pi * (2r)^2 * (2h) = 8 * (1/3) * pi * r^2 * h = 8 * original volume. Increase = 8V - V = 7V, which is 700%.

AI explanation

The volume of a cone is one by three pi r squared h. Increasing the height and the radius by one hundred percent makes them two r and two h, so the new volume is one by three pi times two r squared times two h, which equals eight by three pi r squared h. The increase in volume is eight minus one equals seven times the original volume, meaning the percentage increase is seven hundred percent.

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