Multiple choice

If the ratio of the total surface area to the curved surface area of a cylindrical tank is 5 : 3, then what is the ratio of its height to its diametre?

  1. 1 : 4

  2. 4 : 3

  3. 2 : 5

  4. 3 : 4

  5. 4 : 1
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D Correct answer
Explanation

Total Surface Area (TSA) = 2*pi*r*(r+h). Curved Surface Area (CSA) = 2*pi*r*h. TSA/CSA = (r+h)/h = 5/3. 3r + 3h = 5h. 3r = 2h. h/r = 3/2. Ratio of height to diameter (2r) = h / 2r = 3 / (2*2) = 3/4.

AI explanation

The total surface area of the cylinder is 2 times pi times r times the sum of r and h, while the curved surface area is 2 times pi times r times h. Setting their ratio to 5 to 3 gives r plus h divided by h equals 5 to 3, which means 3r plus 3h equals 5h and thus 3r equals 2h. This means the ratio of height h to radius r is 3 to 2, and since the diameter is 2r, the ratio of height to diameter is 3 to 4. The result is 3 : 4.

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