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 ?

1 Answer
Mar 12, 2018

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 π(2d2)2×kh=πkhd2

and π(3d2)2×h=9π4hd2

As two volumes are equal, we have

πkhd2=9π4hd2

or k=9π4hd2πhd2=9:4

Hence ratio of their heights is 9:4