Multiple choice

Find the percentage increase in the volume of a right circular cone, if its height is decreased by 10% and the radius is increased by 20%.

  1. 18.43%

  2. 25.8%

  3. 29.6%

  4. 12.45%

  5. 16.4%
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C Correct answer
Explanation

Volume V = (1/3) * pi * r^2 * h. New radius r' = 1.2r, new height h' = 0.9h. New volume V' = (1/3) * pi * (1.2r)^2 * (0.9h) = (1/3) * pi * 1.44r^2 * 0.9h = 1.296 * V. The increase is 29.6%.

AI explanation

Using the volume of a cone formula, the new volume is one-third times pi times 1.2r squared times 0.9h, equaling 1.296 times one-third times pi times r squared times h. The percentage increase is calculated as new volume minus original volume divided by original volume times 100, so 1.296 minus 1 divided by 1 times 100 equals 29.6 percent. The percentage increase in the volume of a right circular cone is 29.6 percent.

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