Question

If the radii of two cylinder are in the ratio 2 : 3 and their heights are in the ratio 5 : 3, then find the ratio of their volumes.

Answer 1

Let r₁ and r₂ be the radii of the two cylinders respectively and h₁ and h₂ are the heights of the two cylinders respectively. It is given that `r_1 : r_2 = 2:3` and `h_1 : h_2 = 5:3`

We are asked to find the ratio of the volumes of the two cylinders

Now;

`"Volume of cylinder 1 "/"Volume of cylinder 2" = (pir_1^2h_1)/(pir_2^2 h^2)`

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

                                        `=(2/3)^2(5/3)`

                                       `= 20/27`

Therefore the ratio of the volumes of the tw2o cylinders is  20 : 27