Multiple choice

The ratio of lateral surface area and volume of a cylinder is 1 : 6. What is the value of its total surface area when the ratio of radius to height is 2 : 3?

  1. 2266.5 sq. in

  2. 2262.4 sq. in

  3. 2260.8 sq. in

  4. 2254.6 sq. in
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Lateral surface area is 2*pi*r*h and volume is pi*r^2*h. Ratio (2*pi*r*h) / (pi*r^2*h) = 2/r = 1/6, so r = 12. Given r/h = 2/3, h = 18. Total surface area = 2*pi*r*(r+h) = 2 * 3.1416 * 12 * (12+18) = 2261.95, which is closest to 2260.8.

AI explanation

Using the given ratio of lateral surface area to volume, (2 * pi * r * h) / (pi * r^2 * h) = 1 / 6, which simplifies to 2 / r = 1 / 6 and gives a radius of 12. Because the ratio of radius to height is 2 : 3, the height is 18. The total surface area is 2 * pi * r * (r + h) = 2 * 3.14 * 12 * 30 = 2260.8 sq in.

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