Multiple choice

Two right circular solid cylinder have radii in the ratio $3 : 5$ and heights in the ratio $2 : 3$. Find the ratio between their volumes.

  1. $6 : 25$
  2. $2 : 9$
  3. $6 : 13$
  4. $3 : 17$
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A Correct answer
Explanation

Volume ratio = (pi * r1^2 * h1) / (pi * r2^2 * h2) = (r1/r2)^2 * (h1/h2). Ratio = (3/5)^2 * (2/3) = (9/25) * (2/3) = 18/75 = 6/25.

AI explanation

The volume of a cylinder is found by multiplying pi by the square of the radius and the height, so the ratio of the volumes of the two cylinders is the ratio of the squares of their radii multiplied by the ratio of their heights. Substituting the given ratios gives 3 squared divided by 5 squared times 2 divided by 3, which simplifies to 9 divided by 25 times 2 divided by 3. Multiplying these fractions yields a final volume ratio of 6 to 25.

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