Multiple choice

If the radius of a cylinder is doubled and the height is halved, what is the ratio between the new curved surface area and the previous curved surface area of the cylinder?

  1. $1 : 1$
  2. $2 : 1$
  3. $3 : 2$
  4. $2 : 3$
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A Correct answer
Explanation

Curved surface area (CSA) = 2 * pi * r * h. New radius R = 2r, new height H = h/2. New CSA = 2 * pi * (2r) * (h/2) = 2 * pi * r * h. The ratio is 1:1.

AI explanation

The formula for the curved surface area of a cylinder is 2 * pi * r * h. If the radius is doubled and the height is halved, the new curved surface area is 2 * pi * (2r) * (h / 2). Simplifying this expression results in 2 * pi * r * h, which is identical to the original curved surface area. Therefore, the required ratio is 1 : 1.

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