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Question
If the radii of two cylinder are in the ratio 2 : 3 and their heights are in the ratio 5 : 3, then find the ratio of their volumes.
Solution
Let r1 and r2 be the radii of the two cylinders respectively and h1 and h2 are the heights of the two cylinders respectively. It is given that `r_1 : r_2 = 2:3` and `h_1 : h_2 = 5:3`
We are asked to find the ratio of the volumes of the two cylinders
Now;
`"Volume of cylinder 1 "/"Volume of cylinder 2" = (pir_1^2h_1)/(pir_2^2 h^2)`
`=(r_1/r_2)^2(h_1/h_2)`
`=(2/3)^2(5/3)`
`= 20/27`
Therefore the ratio of the volumes of the tw2o cylinders is 20 : 27
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