Question

Two cylinders of same volume have their radii in the ratio 1 : 6, then ratio of their heights is ______.

Answer 1

Two cylinders of same volume have their radii in the ratio 1 : 6, then ratio of their heights is 36 : 1.

Explanation:

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

Given, `r_1/r_2 = 1/6`

Now, according to the question,

`pir_1^2h_1 = pir_2^2h_2`   ...[∵ Volume of cylinder = πr²h]

⇒ `r_1^2/r_2^2 = h_2/h_1`

⇒ `(r_1/r_2)^2 = h_2/h_1`

⇒ `(1/6)^2 = h_2/h_1`

⇒ `1/36 = h_2/h_1`

or `h_1/h_2 = 36/1`

or h₁ : h₂ = 36 : 1