Question

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

Answer 1

Given data is as follows:

`h_1/h_2 = 1/2`

Volume of cylinder₁ = Volume of cylinder₂

We have to find the ratio of their radii

Since the volumes of the two cylinders are equal,

`"Volume of cylinder"_1/"  Volume of cylinder"_2=1`

`(pir_1^2h_1)/(pir_2^2 h_2 )= 1`

`(r_1/r_2)^2(h_1/h_2)=1`

But it is given that,

`h_1/h_2=1/2`

Therefore,

`(r_1/r_2)^2 xx 1/2 = 1`

          ` (r_1/r_2)^2= 2`

         ` (r_1/r_2)^2 = 2/1`

                `r_1/r_2 = sqrt(2)/1`

Therefore, the ratio of the radii of the two cylinders is `sqrt(2) : 1`