Question

The heights of two circular cylinders of equal volume are in the ratio 1 : 2. The ratio of their radii is

Options

• `1 : sqrt(2)`

• `sqrt(2) : 1`

• 1 : 2

• 1 : 4

Answer 1

`sqrt(2) : 1`

Let the radii of the two cylinders be r and R and their heights be h and 2h, respectively.
Since the volumes of the cylinders are equal, therefore:

`pi xx "r"^2xx"h" = pixx"R"^2xx2"h"`

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

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

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

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

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