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If the length of the radii of two solid ...

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

A

`2:5`

B

`8:7`

C

`10:9`

D

`16:9`

Text Solution

Verified by Experts

The correct Answer is:
C
Let the radii of two solid right circular cylinders are 2x units and 3x units, such that their ratio is `2x:3x=2:3`, which satisfies the given condition. Also let their heights be 5 h units and 3h units respectively.
`:.` the area of the lateral surface of the first `=2pi xx 2x xx 5h` sq-units `=20 pi x h ` sq-units.
and the area of the lateral surface of the second `=2pi xx 3x xx 3h` sq-units `=18pi x h ` sq-units.
Hence the required ratio `=2pi xx h : 18 pi x h = 10:9`
`:.` (c) is correct.
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