The diameter of two cylinder are in the ratio of 2:3. What will be the ratio of their heights if their volumes are equal ?

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Answer 1 · 2018-03-12T15:08:21

Ratio of their heights is #9:4#

Let the ratio of height of two cylinders be #k:1#, say heights are #kh# and #h#

As diameters are in the ratio of #2:3#, let diameters be #2d# and #3d#.

Hence their volumes are #pi((2d)/2)^2xxkh=pikhd^2#

and #pi((3d)/2)^2xxh=(9pi)/4hd^2#

As two volumes are equal, we have

#pikhd^2=(9pi)/4hd^2#

or #k=((9pi)/4hd^2)/(pihd^2)=9:4#

Hence ratio of their heights is #9:4#