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Question
The heights of two circular cylinders of equal volume are in the ratio 1 : 2. The ratio of their radii is
Options
`1 : sqrt(2)`
`sqrt(2) : 1`
1 : 2
1 : 4
Solution
`sqrt(2) : 1`
Let the radii of the two cylinders be r and R and their heights be h and 2h, respectively.
Since the volumes of the cylinders are equal, therefore:
`pi xx "r"^2xx"h" = pixx"R"^2xx2"h"`
`=> "r"^2/"R"^2 = 2/1`
`=> ("r"/"R")^2 = 2/1`
`=> "r"/"R" = sqrt(2)/1`
`=> "r":"R" = sqrt(2:1)`
Hence, the ratio of their radii is `sqrt(2 : 1)`
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