Multiple choice

The diameter of a right circular cylinder increases by $50$% and its height decreases by $40$%, then finds the percentage change in its curved surface area.

  1. $20$% decrease
  2. $10$% decrease
  3. $10$% increase
  4. $20$% increase
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Curved surface area S = 2*pi*r*h. New radius r' = 1.5r. New height h' = 0.6h. New area S' = 2*pi*(1.5r)*(0.6h) = 0.9 * (2*pi*r*h) = 0.9S. This is a 10% decrease.

AI explanation

The curved surface area of a cylinder is calculated as 2 * pi * r * h. A 50% increase in diameter means the radius becomes 1.5r, while a 40% decrease in height makes it 0.6h, resulting in a new curved surface area of 2 * pi * 1.5r * 0.6h. This equals 0.9 times the original area, indicating a 10% decrease.

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