Multiple choice

The radius and the height of a cone are both increased by 20%. The volume of the cone is increased by

  1. 172.8%

  2. 272.8%

  3. 72.8%

  4. 100%

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Volume V = (1/3) * pi * r^2 * h. New volume V' = (1/3) * pi * (1.2r)^2 * (1.2h) = (1/3) * pi * 1.44 * r^2 * 1.2 * h = 1.728 * V. The increase is 1.728 - 1 = 0.728, or 72.8%.

AI explanation

Using the volume of a cone formula, one-third times pi times radius squared times height, the initial volume is directly proportional to the product of the radius squared and the height. Increasing the radius and height by 20 percent makes the new radius 1.2 times the original and the new height 1.2 times the original. The new volume becomes one-third times pi times the quantity 1.2 times the original radius squared times the quantity 1.2 times the original height, which simplifies to 1.2 cubed, or 1.728, times the original volume. This means the volume increases by 72.8 percent.

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