Question
The height of two right circular cones are in the ratio 1 : 2 and the perimeters of their bases are in the ratio 3 : 4 . Find the ratio of their volumes .
Answer: Option A
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Let the radii of their bases be r and R and their height be h and 2 h respe4ctively .
Then , `(2pir)/(2piR) = 3/4 `
`rArr r/R = 3/4 `
`R = 4/3 r`
`:.` Ratio of volumes = `(1/3 pi r^2 h)/(1/3 pi (4/3 r)^2 2h)` = ` 9 /32 ` = 9 : 32
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