Question

Two circular cylinders of equal volumes have their heights in the ratio 1 : 2. Find the ratio of their radii.

Answer 1

Here, V₁ = Volume of cylinder 1
         V₂ = Volume of cylinder 2
          r₁ = Radius of cylinder 1
          r₂ = Radius of cylinder 2
          h₁ = Height of cylinder 1
          h₂ = Height of cylinder 2

Volumes of cylinder 1 and 2 are equal.
Height of cylinder 1 is half the height of cylinder 2.
​∴ V₁ = V₂
(πr₁²h₁) = (πr₂²h₂) 
(πr₁²h) = (πr₂²2h) 

\[\frac{{r_1}^2}{{r_2}^2} = \frac{2}{1}\]

\[\frac{r_1}{r_2} = \sqrt{\frac{2}{1}}\]

Thus, the ratio of their radii is \[\sqrt{2}\]:1