The diameter of two cylinders are in the ratio 5 : 4, and their v

| The diameter of two cylinders are in the ratio 5 : 4, and their volumes are in the ratio 3 : 4 so, their heights will be in the ratio

A. 4 : 9

B. 12 : 25

C. 9 : 16

D. 16 : 25

Please scroll down to see the correct answer and solution guide.

We know that,

Volume of a cylinder = πr²h

Where, r = Radius of the cylinder, h = Height of the cylinder

Let the diameters and heights of two cylinders be d₁, d₂ and h₁, h₂ respectively.

Volume of one cylinder = πd₁²h₁/4

Volume of other cylinder = πd₂²h₂/4

⇒ Ratio of volumes of the cylinders = 3/4

⇒ d₁²h₁/d₂²h₂ = 3/4

⇒ h₁/h₂ = (3/4) × (16/25) = 12/25

∴ Ratio of their heights = 12 : 25