If the length of the radii of two solid right circular cylinder are in the ratio 2:3 and their height are in the ratio 5:3 , then the ratio of their volumes is

Options

A. `27:20`
B. `20:27`
C. `4:9`
D. `9:4`

Answer

B

Explanation

Let the radii are 2r units and 3r units and their heights are 5 h units and 3h units respectively.
Then the volume of the first `= pi (2r)^(2) xx 5h ` cubic-units `= 20 pi r^(2)h` cubic-units
and the volume of the second `= pi (3r)^(2)xx 3h` cubic-units `= 27 pi r^(2)h` cubic-units.
Hence the required ratio `= 20 pi r^(2)h : 27 pi r^(2) h = 20 :27`
`:.` (b) is correct.