If the radii of two cylinders are in the ratio 2:3 and their heights are in the ratio 5:3, then find the ratio of their volumes.

Options

A. `10:17`
B. `20:27`
C. `17: 27`
D. `20: 37`

Answer

B

Explanation

Let the radii of two cylinders be `r_(1)` and `r_(2)` and height of the cylinder be `h_(1)` and `h_(2)`
Given , `" "(r_(1))/(r_(2)) =(2)/(3) and (h_(1))/(h_(2)) = (5)/(3)`
`therefore`Ratio of volumes `(pir_(2)^(1) h_(1))/(pir_(2)^(2) h_(2)) =((r_(1))/(r_(2)))^(2)((h_(1))/(h_2))`
`= ((2)/(3))^(2)((5)/(3)) =(4)/(9) xx (5)/(3) = 20: 27`
Hence, the radius of their volumes is 20: 27