Multiple choice

If the radius of a cylinder is decreased by 50% and the height is increased by 50%, then what is the change in the volume?

  1. 67.5% increase

  2. 62.5% increase

  3. 67.5% decrease

  4. 62.5% decrease
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Volume V = pi * r^2 * h. New radius r' = 0.5r, new height h' = 1.5h. New volume V' = pi * (0.5r)^2 * (1.5h) = pi * 0.25r^2 * 1.5h = 0.375 * V. The change is (0.375 - 1) * 100 = -62.5%.

AI explanation

Let the initial radius be r and initial height be h, so the original volume is pi times r squared times h. The new radius is 0.5r and the new height is 1.5h, making the new volume pi times 0.25r squared times 1.5h, which equals 0.375 times pi r squared h. The change in volume is 1 minus 0.375, resulting in a 0.625 or 62.5 percent decrease.

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