The radii of two right circular cylinder are in the ratio 2:3 and their heights are in the ratio 5:4. Calculate the ratio of their curved surface areas and also the ratio of their volumes.

Explanation

Let the radius of first cylinder be `r_1` and height be `h_1`
Let the radius of second cylinder be `r_2` and height be `h_2`
According to question:
`r_1/r_2=2/3` and `h_1/h_2=5/4`
Curved surface area of first cylinder `S_1=2pir_1h_1`
Curved surface area of second cylinder `S_2=2pir_2h_2`
Then,
`S_1/S_2=(2pir_1h_1)/(2pir_2h_2)=(r_1/r_2)(h_1/h_2)=(2/3)(5/4)=5/6`
`S_1:S_2=5:6`
`therefore` The ratio of their curved surface areas`=5:6`
The ratio of their volume:
`V_1/V_2=(pir_1^2h_1)/(pir_2^2h_2)=(r_1/r_2)^2(h_1/h_2)=(2/3)^2⋅(5/4)=4/9xx5/4=5/9`
`V_1:V_2=5:9`
`therefore` The ratio of their volumes`=5:9`