Question

diameter of two cylinder are in the ratio of 2 ratio 3 find the ratio of their height if their volume is same ​

Answer 1

The ratio of the diameters of the cylinders = 2 : 3

⇒ The ratio of the radius of the cylinders will be = 2 : 3

Therefore, let the radii of the two cylinder be 3x and 2x respectively.

Let the height of the cylinder be h1 and h2.

Volume of first cylinder = Volume of the second cylinder

π(2x)²h2  =  π(3x)²h1

h1/h2 = (π x 9x²)/(π x 4x²)

h1/h2 = 9/4

h1 : h2 = 9 : 4

So, ratio of their heights is 9 : 4