Multiple choice

State true or false: The radius of a solid right circular cylinder decreases by $20\%$ and its height increases by $10\%$. Find the percentage change in its volume Answer: Decrease 29.6%

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Volume V = pi * r^2 * h. New radius = 0.8r, new height = 1.1h. New Volume = pi * (0.8r)^2 * (1.1h) = pi * 0.64r^2 * 1.1h = 0.704 * V. Change = 1 - 0.704 = 0.296, which is a 29.6% decrease.

AI explanation

The original volume of the cylinder is V = pi * r^2 * h. The new radius is 0.8r and the new height is 1.1h, making the new volume V' = pi * (0.8r)^2 * 1.1h = 0.704 * pi * r^2 * h. The ratio of the new volume to the old volume is 0.704, which represents a 29.6% decrease in volume. The statement is True.

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