Question

Two right circular cylinders of equal volumes have their heights in the ratio 1 : 2. What is the ratio of their radii?

Answer 1

Let the radii of the two cylinders be r and R; and height be h and we have,

`"h"/"H" = 1/2`          ...........(i)

Volume of the first cylinder = Volume of the second sphere

⇒ πr² H = πR² H

`⇒ "h"/"H" = "R"^2/"r"^2`

`=> 1/2 = "R"^2/"r"^2`

`=> "r"^2/"R"^2 = 1/2`

`=> ("r"/"R")^2=1/2`

`=>"r"/"R" = sqrt(2/1)`

`∴ "r" : "R" =sqrt(2:1)`

So, the ratio of their radii is `sqrt(2)` : 1.