Question

There are two cylinders they are similar.

The ratio of their volumes is 8:27
The height of one cylinder is 8
Find second cylinders height

Answer 1

height of second cylinder = 12

Explanation:

given similar cylinders , then if

ratio of heights = a : b , then

ratio of volume = a³ : b³

here we are given ratio of volumes = 8 : 27 , then

ratio of heights =
`\sqrt[3]{8}` :
`\sqrt[3]{27}` = 2 : 3

let h be height of the second cylinder then by proportion

`(ratio)/(height)`

`(2)/(8)` =
`(3)/(h)` ← cross- multiply

2h = 8 × 3 = 24 ( divide both sides by 2 )

h = 12

height of second cylinder is 12 units