Multiple choice

Two right circular cylinders of equal volume have their heights in the ratio of $4:9$. Find the ratio of their curved surface areas.

  1. $9:4$
  2. $2:3$
  3. $4:9$
  4. $3:2$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Volume V = pi * r^2 * h. Since volumes are equal, r1^2 * h1 = r2^2 * h2. Given h1/h2 = 4/9, then r1^2 / r2^2 = 9/4, so r1/r2 = 3/2. Curved surface area S = 2 * pi * r * h. Ratio S1/S2 = (r1 * h1) / (r2 * h2) = (3/2) * (4/9) = 12/18 = 2/3.

AI explanation

Since the cylinder volumes are equal, pi * r1^2 * h1 = pi * r2^2 * h2, meaning r1^2 * 4 = r2^2 * 9, so the radii are in the ratio 3:2. The curved surface area formula is 2 * pi * r * h, so the ratio of the areas is (3 * 4) : (2 * 9), which simplifies to 12 : 18, or 2:3.

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