Question

Two cylinders of equal volume have heights in the ratio 1 : 9. The ratio of their radii is ______.

Answer 1

Two cylinders of equal volume have heights in the ratio 1 : 9. The ratio of their radii is 3 : 1.

Explanation:

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

Given, `h_1/h_2 = 1/9`

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 = 9/1`

⇒ `r_1/r_2 = sqrt(9)/1`

⇒ `r_1/r_2 = 3/1`

Hence, r₁ : r₂ = 3 : 1