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 $9 : 4$ $9:4$

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

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

Hence their volumes are $π {(\frac{2 d}{2})}^{2} \times k h = π k h d^{2}$ $pi((2d)/2)^2xxkh=pikhd^2$

and $π {(\frac{3 d}{2})}^{2} \times h = \frac{9 π}{4} h d^{2}$ $pi((3d)/2)^2xxh=(9pi)/4hd^2$

As two volumes are equal, we have

$π k h d^{2} = \frac{9 π}{4} h d^{2}$ $pikhd^2=(9pi)/4hd^2$

or $k = \frac{\frac{9 π}{4} h d^{2}}{π h d^{2}} = 9 : 4$ $k=((9pi)/4hd^2)/(pihd^2)=9:4$

Hence ratio of their heights is $9 : 4$ $9:4$