Multiple choice

The radius of a right circular cylinder is increased by 25%. The volume will stay the same if the height is

  1. increased by 64%

  2. decreased by 36%

  3. decreased by 25%

  4. increased by 25%

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

V = pi * r^2 * h. New radius = 1.25r. New volume = pi * (1.25r)^2 * h_new = pi * 1.5625 * r^2 * h_new. For V to remain constant, 1.5625 * h_new = h. h_new = h / 1.5625 = 0.64h. This is a 36% decrease.

AI explanation

If the radius is increased by 25 percent, the new radius is 1.25 times the original, making the new squared radius 1.5625 times the original. For the volume of the cylinder to remain the same, the height multiplied by 1.5625 must equal the original height, meaning the new height is 1 divided by 1.5625, or 0.64, times the original. This means the height is decreased by 36 percent. The correct answer is decreased by 36 percent.

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