Question

The heights of two cylinders are in the ratio of 5:3 and their volume are in the ratio 20:27. then the ratio of their radius is...... ?

plz its urgent

Answer 1

The ratio of their radius is
`2:3`

Explanation:

Volume of cylinder is
`\pi r^2h`, where r is radius and h is height

We have

The heights of two cylinders are in the ratio of
`5:3`

`(h_1)/(h_2) =(5)/(3)`

The volume are in the ratio
`20:27`

`(V_1)/(V_2) =(20)/(27)\\\\(\pi r_1^2h_1)/(\pi r_2^2h_2) =(20)/(27)\\\\( r_1^2)/( r_2^2)* (3)/(5) =(20)/(27)\\\\( r_1^2)/( r_2^2) =(4)/(9)\\\\( r_1)/( r_2) =(2)/(3)`

The ratio of their radius is
`2:3`

Answer 2

2 : 3

Explanation:

Let,

Radius of cylinder 1 = R

Radius of cylinder 2 = r

Now,

We know that

Volume of cylinder = πr²h

=> πR²h/πr²h' = 20/27

=> R² × 5/r² × 3 = 20/27

=> R²/r² = 20/27 × 3/5

=> R²/r² = 4/9

=> R/r = √(4/9)

=> R/r = 2/3

=> R : r = 2 : 3