Multiple choice

The ratio of the height of a circular cylinder to the diameter of its base is $1:2$. Then the ratio of the areas of its curved surface to the sum of the areas of its two ends is:

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

Height h, diameter d = 2r. Ratio h:d = 1:2 implies h = r. Curved surface area = 2 * pi * r * h = 2 * pi * r^2. Sum of areas of two ends = 2 * pi * r^2. Ratio = 1:1.

AI explanation

Let the height of the cylinder be r, which makes the diameter of its base 2r and its radius r. The curved surface area is 2 * pi * r * h, which becomes 2 * pi * r * r, or 2 * pi * r^2. The sum of the areas of its two ends is 2 * pi * r^2. Therefore, the ratio of the curved surface area to the sum of the areas of the two ends is 1:1.