The radii of two cylinders are in the ratio 2 : 3 and their heights are in the ratio 5 : 3. Calculate the ratio of their volumes and the ratio of their curved surfaces.
Solution
Data given is as follows:
Ratio of radii of two cylinders = 2:3
Ratio of heights of two cylinders = 5:3
We have to find out the following:
(i) Ratio of the volumes of the two cylinders
(ii) Ratio of the Curved Surface Area of the two cylinders
Let `r_1`and `r_2`be the radii of the two cylinders respectively.
Let `h_1` and `h_2`be the heights of the two cylinders respectively.
Therefore we have,
`r_1/r_2 = 2/3`
`h_1/h_2 = 5/3`
(i) Since we have to find the ratio of the volumes of the two cylinders, we have
`("Volume of cylinder 1")/("Volume of cylinder 2") = (pi r_1^2h_1)/(pir_2^2h_2)`
`=(r_1/r_2)^2 (h_1/h_2)`
`=(2/3)^2 (5/3)`
`("Volume of cylinder 1")/("Volume of cylinder 2") = (20/27)`
(ii) Since we have to find the ratio of the curved surface areas of the two cylinders, we have,
`("Curved Surface Area of cylinder 1")/("Curved Surface Area if cylinder 2") = (2pir_1h_1)/(2pir_2h_2)`
`=(r_1/r_2) (h_1/h_2)`
`=(2/3)(5/3)`
`("Curved Surface Area of cylinder 1")/("Curved Surface Area if cylinder 2") = (10/9)`
