Multiple choice

The radius of two cylinders are in the ratio $2:3$ and their heights are in the ratio $3:5$. Find the ratio of their volumes.

  1. $\dfrac{2}{3}$
  2. $\dfrac{3}{5}$
  3. $\dfrac{4}{15}$
  4. $\dfrac{3}{2}$
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C Correct answer
Explanation

Volume ratio = (r1^2 * h1) / (r2^2 * h2) = (2^2 * 3) / (3^2 * 5) = (4 * 3) / (9 * 5) = 12 / 45 = 4 / 15.

AI explanation

The volume of a cylinder is pi*r^2*h. If the radii are in the ratio 2:3 and the heights are in the ratio 3:5, their volumes are in the ratio pi*2^2*3 : pi*3^2*5. Simplifying this gives 12*pi : 45*pi, which reduces to 4:15.

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