Multiple choice

The ratio between the curved surface area and the total surface area of a right circular cylinder is 2 : 3. What is the respective ratio between the height and the radius of the cylinder?

  1. 1 : 2

  2. 2 : 1

  3. 1 : 3

  4. 3 : 1
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

CSA = 2*pi*r*h. TSA = 2*pi*r*h + 2*pi*r^2. Ratio CSA/TSA = h / (h + r) = 2/3. 3h = 2h + 2r => h = 2r. Ratio h/r = 2/1.

AI explanation

The curved surface area is 2 times pi times r times h and the total surface area is 2 times pi times r times the sum of r and h. Setting their ratio to 2 to 3 allows the cancellation of 2 times pi times r, leaving h divided by the sum of r and h equal to 2 divided by 3. Cross-multiplying yields 3h equals 2r plus 2h, which simplifies to h equals 2r. The respective ratio between the height and the radius is 2 to 1.

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