Multiple choice

If the radius of a cylinder is increased by 25%, then by what percent must the height be reduced so that the volume of the cylinder remains the same?

  1. 36%

  2. 56%

  3. 64%

  4. 46%
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A Correct answer
Explanation

Volume V = pi * r^2 * h. If r increases by 25%, the new radius is 1.25r. The new volume is pi * (1.25r)^2 * h_new = pi * 1.5625 * r^2 * h_new. For V to be constant, 1.5625 * h_new = h, so h_new = h / 1.5625 = 0.64h. The reduction is 1 - 0.64 = 0.36, or 36%.

AI explanation

The volume of a cylinder is found using the formula pi times radius squared times height. If the radius is increased by 25 percent, the new radius is 1.25 times the original radius, meaning the radius squared becomes 1.5625 times its original value. To keep the volume constant, the new height must be 1 divided by 1.5625, which is 0.64 of the original height. This represents a reduction of 36 percent.

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