Multiple choice

In case of a right circular cylinder the radius of base and height are in the ratio $2:3$. Therefore, the ratio of lateral surface area to the total surface area is

  1. $5:3$
  2. $3:5$
  3. $2:5$
  4. $2:3$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Radius r = 2k, height h = 3k. Lateral Surface Area (LSA) = 2 * pi * r * h = 2 * pi * (2k) * (3k) = 12 * pi * k^2. Total Surface Area (TSA) = LSA + 2 * pi * r^2 = 12 * pi * k^2 + 2 * pi * (2k)^2 = 12 * pi * k^2 + 8 * pi * k^2 = 20 * pi * k^2. Ratio LSA/TSA = 12/20 = 3/5.

AI explanation

Let the radius be 2x and the height be 3x based on the given ratio. The lateral surface area is 2 * pi * r * h = 2 * pi * 2x * 3x = 12 * pi * x^2. The total surface area is 2 * pi * r * (r + h) = 2 * pi * 2x * (2x + 3x) = 20 * pi * x^2. The ratio of lateral surface area to total surface area is 12 * pi * x^2 : 20 * pi * x^2, which simplifies to 3:5.

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