Multiple choice

What is the ratio between the curved surface area of a cylinder and a sphere of the same radius, if height of the cylinder is twice of radius?

  1. 1 : 1

  2. 3 : 1

  3. 4 : 1

  4. 5 : 1

  5. None of these
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A Correct answer
Explanation

Curved surface area of cylinder = 2 * pi * r * h. Since h = 2r, area = 4 * pi * r^2. Surface area of sphere = 4 * pi * r^2. The ratio is 1:1.

AI explanation

The curved surface area of a cylinder is calculated using the formula 2 * pi * r * h, and since the height is twice the radius, we substitute h with 2r to get an area of 4 * pi * r^2. The surface area of a sphere with the same radius is 4 * pi * r^2. Comparing the two equal expressions gives a ratio of 1 : 1.

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