Multiple choice

The radius of a cylinder is increased by 120% and its height is decreased by 40%. What is the percentage increase in its volume?

  1. 180.6%

  2. 212.8%

  3. 190.4%

  4. 175.4%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Volume of a cylinder is V = pi * r^2 * h. If radius increases by 120%, the new radius is 2.2r. If height decreases by 40%, the new height is 0.6h. The new volume is pi * (2.2r)^2 * (0.6h) = pi * 4.84r^2 * 0.6h = 2.904 * V. This represents a 190.4% increase.

AI explanation

The initial volume of the cylinder is given by the formula V = πr^2h. When the radius is increased by 120%, the new radius becomes 2.2 times the original radius, and when the height is decreased by 40%, the new height becomes 0.6 times the original height. The new volume is π * (2.2r)^2 * (0.6h) = 2.904πr^2h, showing that the new volume is 2.904 times the original volume. To find the percentage increase, subtract the original 1 from 2.904 to get a 1.904 increase, and multiplying by 100 results in a 190.4% increase.

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