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

If volumes of two solid right circular cylinders are same and their he

1.	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 -A. `1 : sqrt(2)`B. `sqrt(2):1`C. `1:2`D. `2:1`
Answer» Correct Answer - B 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.