Multiple choice

If the radius of a cylinder is decreased by 20% and the height is increased by 20% to form a new cylinder, then the volume will be decreased by:

  1. 23.2%

  2. 22.3%

  3. 32.2%

  4. 20.5%
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A Correct answer
Explanation

Volume V = pi*r^2*h. New radius r' = 0.8r, new height h' = 1.2h. New volume V' = pi*(0.8r)^2*(1.2h) = pi*0.64*r^2*1.2*h = 0.768*V. Decrease = 1 - 0.768 = 0.232 or 23.2%.

AI explanation

The original volume of the cylinder is πr²h. The new volume with the adjusted dimensions is π(0.8r)²(1.2h) = π(0.64r²)(1.2h) = 0.768πr²h. This represents a decrease of 1 - 0.768 = 0.232, which is a 23.2% decrease in volume.

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