Multiple choice

On increasing each of the radius of the base and the height of a cone by $20\%$ its volume will be increased by

  1. $20$%
  2. $40$%
  3. $72.2$%
  4. $72.8$%
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 * (1.2r)^2 * (1.2h) = (1/3) * pi * 1.44r^2 * 1.2h = 1.728 * V. Increase = 72.8%.

AI explanation

Let the original radius and height of the cone be r and h, giving an initial volume of one third times pi times r squared times h. A 20 percent increase means the new radius is 1.2r and the new height is 1.2h, making the new volume one third times pi times 1.2r squared times 1.2h, which simplifies to 1.728 times the original volume. The percentage increase in the volume is therefore (1.728 minus 1) times 100, resulting in 72.8 percent.

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