Multiple choice

A right circular cone has a base radius of $r$ and a height of $h.$ If the radius decrease by $20$ percent and the height increase by $10$ percent, which of the following is the resulting percent change in the volume of the cone?

  1. $10$% decrease
  2. $12$% decrease
  3. $18.4$% decrease
  4. $29.6$% decrease
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Volume V = (1/3) * pi * r^2 * h. New volume V' = (1/3) * pi * (0.8r)^2 * (1.1h) = (1/3) * pi * 0.64r^2 * 1.1h = 0.704 * V. This is a 29.6% decrease.

AI explanation

Using the cone volume formula of one third times pi times r squared times h, the new volume becomes one third times pi times (0.8r) squared times (1.1h), equaling 0.704 times the original volume. This is a decrease of 1 minus 0.704, which equals 0.296, representing a 29.6 percent decrease in volume.

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