Question : The radii of two cylinders are in the ratio 2 : 3 and their heights are in the ratio 5 : 3. The ratio of their volumes is _______.
Option 1: 27 : 20
Option 2: 20 : 27
Option 3: 4 : 9
Option 4: 9 : 4
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Correct Answer: 20 : 27
Solution : The radii of two cylinders are in the ratio 2 : 3 and their heights are in the ratio 5 : 3. Let the radius, $r_1$ of the 1st cylinder be $2m$ and height, $h_1$ be $5n$. Let the radius, $r_2$ of the 2nd cylinder be $3m$ and height, $h_2$ be $3n$. According to the question, Volume of the 1st cylinder : Volume of the 2nd cylinder $=\pi r_1^2 h_1:\pi r_2^2 h_2$ $={r_1^2 h_1}:{r_2^2 h_2}$ $=(2m)^2×5n:(3m)^2×3n$ $=20m^2n:27m^2n$ $=20:27$ Hence, the correct answer is 20 : 27.
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