Multiple choice

The radius of base of a right circular cylinder is halved and its height is increased by 50%. The ratio of volume of the new cylinder to that of the original cylinder will be

  1. 3 : 8

  2. 2 : 1

  3. 3 : 1

  4. 4 : 1
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A Correct answer
Explanation

V = pi * r^2 * h. New radius r' = r/2, new height h' = 1.5h. New volume V' = pi * (r/2)^2 * (1.5h) = pi * (r^2/4) * (3h/2) = (3/8) * pi * r^2 * h. Ratio = 3/8.

AI explanation

Using the cylinder volume formula V = pi * r^2 * h, the new radius is r/2 and the new height is 1.5h. The new volume becomes pi * (r/2)^2 * 1.5h, which simplifies to 1.5/4 times the original volume. This results in a ratio of 3 : 8 for the new volume to the original volume.

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