Question

The radii of two cylinders are in the ratio 2 : 3 and their heights are in the ratio 5 : 3. Calculate the ratio of their volumes.

Answer 1

Here, r₁ = Radius of cylinder 1
h₁ = Height of cylinder 1
r₂ = Radius of cylinder 2
h₂ = Height of cylinder 2
V₁ = Volume of cylinder 1
V₂ = Volume of cylinder 2
Ratio of the radii of two cylinders = 2:3
Ratio of the heights of two cylinders = 5:3

Volume of the cylinder = πr²h
V₁/V₂ = (πr₁²h₁)/(πr₂²h₂) = (π(2r)²5h)/(π(3r)²3h)
V₁/V₂ = (π4r²5h)/(π9r²3h) = 20 / 27
Hence, the ratio of their volumes is 20:27