Multiple choice

In a cylindrical tank, the height is 1.5 times the radius of its base. What is the ratio of the curved surface area (CSA) to the total surface area (TSA) of the cylinder?

  1. 3 : 2

  2. 2 : 3

  3. 5 : 3

  4. 3 : 5

Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

CSA = 2 * pi * r * h. TSA = 2 * pi * r * (r + h). Given h = 1.5r. CSA = 2 * pi * r * 1.5r = 3 * pi * r^2. TSA = 2 * pi * r * (r + 1.5r) = 2 * pi * r * 2.5r = 5 * pi * r^2. Ratio CSA/TSA = 3/5.

AI explanation

Let the radius be r, which makes the height 1.5r. The curved surface area is 2 times pi times r times h, which equals 2 times pi times r times 1.5r, or 3 times pi times r squared. The total surface area is 2 times pi times r times (h plus r), resulting in 2 times pi times r times 2.5r, which is 5 times pi times r squared. The ratio of curved surface area to total surface area is 3 to 5.