Question

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 ?

Answer 1

Ratio of their heights is `9:4`

Explanation:

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`