Multiple choice

If the curved surface area of a solid cylinder is one-third of its total surface area, then what is the ratio of its diameter to its height?

  1. 5 : 2

  2. 1 : 1

  3. 2 : 1

  4. 4 : 1
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D Correct answer
Explanation

Curved surface area (CSA) = 2*pi*r*h. Total surface area (TSA) = 2*pi*r*h + 2*pi*r^2. Given CSA = 1/3 TSA, then 3*CSA = TSA, so 6*pi*r*h = 2*pi*r*h + 2*pi*r^2. This simplifies to 4*pi*r*h = 2*pi*r^2, so 2h = r. Diameter d = 2r = 4h. Thus, d/h = 4/1.

AI explanation

The curved surface area of the cylinder is 2 times pi times r times h, which is one third of the total surface area of 2 times pi times r times the sum of r and h. Setting them in a one to three ratio gives 3 times h equals r plus h, which simplifies to 2h equals r. Since the diameter is 2r, substituting r gives the diameter as 4h. The result is 4 : 1.

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