Question

the diameter of two cylinders are in the ratio of 2:3 find the ratio of the Other Heights if their volumes are equal​

Answer 1

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

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

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

Let the height of the cylinder be h1 and h2.

Now, Volume of first cylinder = Volume of the second cylinder

i.e. π(3x)²h1 = π(2x)²h2

h1/h2 = (π*4x²)/(π*9x²)

h1/h2 = 4/9

h1 : h2 = 4 :9

So, ratio of their heights is 4 : 9