If volumes of two solid right circular cylinders are same and their heights are in the ratio 1:2, then the ratio of lengths of their radii is -

Options

A. `1 : sqrt(2)`
B. `sqrt(2):1`
C. `1:2`
D. `2:1`

Answer

B

Explanation

Let the heights of the cylinders are h units and 2h units ( since the ratio is 1:2 ) and let the radii of the cylinders are R and r units respectively.
Since the volume of the cylinders are same,
`:. pi R^(2) h = pi r^(2) .2h rArr R^(2)=2r^(2) rArr sqrt(R^(2))=sqrt(2r^(2))` [ Taking square root of both the sides ]
`rArr R=sqrt(2) r rArr (R)/(r) = sqrt(2) rArr R:r = sqrt(2) :1`
Hence the required ratio `=sqrt(2):1`
`:.` (b) is correct.