Question

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

Answer 1

Let the radii of the cylinders be r₁ and r₂ and their heights be h₁ and h₂ .

We have,

`"r"_1: "r"_2 = 2 : 3 or "r"_1/"r"_2 = 2/3`    ...........(i)

and `"h"1 : "h"2 = 5 : 3 or "h"_1 /"h"_2 = 5/3 ........(ii)`

Now,

The ratio of the volumes of the cylinders `="Volume of the first cylinder"/"Volume of the second cylinder"`

`= (pi"r"_1^2"h"_1)/(pi"r"_2^2"h"_2)`

`= (("r"_1)/"r"_2)^2xx"h"_1/"h"_2`

`= (2/3)^2xx5/3`          [Using (i) and (ii)]

`=20/27`

= 20 : 27

So, the ratio of the volumes of the given cylinders is 20 : 27.