Question : If the heights of two cylinders are in the ratio of 2 : 3 and their radii are in the ratio of 6 : 5, then what is the ratio of the volumes of the cylinders?
Option 1: 24 : 29
Option 2: 21 : 31
Option 3: 24 : 25
Option 4: 28 : 31
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Correct Answer: 24 : 25
Solution : Let the heights of the cylinders be $2x$ and $3x$ and radii be $6y$ and $5y$ respectively. Volume of 1st cylinder : Volume of 2nd cylinder $=\pi r_1^2h_1:\pi r_2^2h_2$ $=\pi \times (6y)^2\times 2x:\pi \times(5y)^2\times3x$ $=36y^2\times 2x:25y^2\times3x$ $=72:75$ $=24 : 25$ Hence, the correct answer is 24 : 25.
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