Multiple choice

The curved surface area of a cylinder is five times the area of its base. Find the ratio of the radius and height of the cylinder.

  1. 2 : 3

  2. 3 : 5

  3. 2 : 5

  4. 3 : 4
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C Correct answer
Explanation

The curved surface area of a cylinder is given by 2 * pi * r * h, and the area of its base is pi * r^2. Setting the curved surface area equal to five times the base area gives 2 * pi * r * h = 5 * pi * r^2, which simplifies to 2h = 5r. Rearranging this equation to find the ratio of radius to height (r/h) yields 2/5, or 2 : 5.

AI explanation

The formula for the curved surface area of a cylinder is 2πrh, and the area of its base is πr². Setting the curved surface area to five times the base area gives the equation 2πrh = 5πr². Dividing both sides by πr yields the ratio of height to radius as h/r = 2/5, so the ratio of radius to height is 2 : 5.

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