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Question

A cylinder and a cone have equal base and heights if their curved surfaces are in the ratio 8:5, Show that ratio of radius and their base to their height is 3:4.

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Solution

Let the radius and height of cylinder and cone be r and h.
Let the slant height of cone be l.
We know that,
Curved surfaces areas of cylinder =2πrh
Curved surfaces of cone =πrl
Ratio =Curved surfaces ares of cylinder/curved surfaces area of cone==2πrhπrl=85
rh=34
Hence,
ratio of radius to height is 3:4

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