Multiple choice

The radius of a solid right circular cylinder decreases by $20\%$ and its height increases by $10\%$. Find the percentage change in its curved surface area

  1. Decrease $ =$ $19\%$
  2. Decrease $ =$ $12\%$
  3. Decrease $ =$ $15\%$
  4. Decrease $ =$ $13\%$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Curved surface area S = 2 * pi * r * h. If r decreases by 20% (new r = 0.8r) and h increases by 10% (new h = 1.1h), the new area S' = 2 * pi * (0.8r) * (1.1h) = 0.88 * (2 * pi * r * h) = 0.88S. This represents a 12% decrease.

AI explanation

The curved surface area of a cylinder is given by the formula 2 * pi * r * h. The new radius becomes 0.80r and the new height becomes 1.10h, making the new curved surface area 2 * pi * 0.80r * 1.10h, which equals 0.88 times the original curved surface area. This results in a 12% decrease in the total curved surface area.

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