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Question
A cylinder and a cone have equal radii of their bases and equal heights. If their curved surface areas are in the ratio 8:5, show that the radius of each is to the height of each as 3:4.
Solution
Let us assume radius of cone=r.
Also, radius of cylinder=r.
And, height of cylinder=h.
Let` C_1` , be the curved surface area of cone
`∴ C_1=pirsqrt(r^2+h^2)`
Similarly,` C_2` be the curved surface area of cone cylinder.
`∴ C_2=2pirh`
According to question `C_2/C_1=8/5`
⇒ `(2pirh)/(pirsqrt(r^2+h^2))=8/5`
⇒ `10h=8sqrt(r^2+h^2)`
⇒ `100h^2=64r^2+64h^2`
⇒ `36h^2=64r^2`
`h/r=sqrt64/30`
⇒`(h/r)^2=64/36`
⇒` b/r=sqrt64/30=8/6=4/3`
`∴ r/h=3/4`
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