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Question
Two circular cylinders of equal volumes have their heights in the ratio 1 : 2. Find the ratio of their radii.
Solution
Given data is as follows:
`h_1/h_2 = 1/2`
Volume of cylinder1 = Volume of cylinder2
We have to find the ratio of their radii
Since the volumes of the two cylinders are equal,
`"Volume of cylinder"_1/" Volume of cylinder"_2=1`
`(pir_1^2h_1)/(pir_2^2 h_2 )= 1`
`(r_1/r_2)^2(h_1/h_2)=1`
But it is given that,
`h_1/h_2=1/2`
Therefore,
`(r_1/r_2)^2 xx 1/2 = 1`
` (r_1/r_2)^2= 2`
` (r_1/r_2)^2 = 2/1`
`r_1/r_2 = sqrt(2)/1`
Therefore, the ratio of the radii of the two cylinders is `sqrt(2) : 1`
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