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Question
The radii of the base of a cylinder and a cone are in the ratio 3 : 4. If their heights are in the ratio 2 : 3, the ratio between their volumes is
Options
9 : 8
3 : 4
8 : 9
4 : 3
Solution
9 : 8
Let the radii of the base of the cylinder and cone be 3r and 4r and their heights be 2h and 3h, respectively.
Then, ratio of their volumes`= (pi(3"r")^2xx(2"h"))/(1/3 pi(4"r")xx(3"h"))`
`=(9"r"^2xx2xx3)/(16"r"^2xx3`
`=9/8`
= 9 : 8
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