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प्रश्न
If the volumes of two cones are in the ratio of 1:4 and their diameters are in the ratio of 4:5, then find the ratio of their heights.
उत्तर
Let r and R be the base radii, h and H be the heights , v and
We have,
`(2r)/(2R) = 4/5 or r/R = 4/5` ............(i)
and
`v/V = 1/4`
`rArr ((1/3pir^2h))/((1/3piR^2H))=1/4`
`rArr ((r^2h))/((R^2H)) = 1/4`
`rArr (r/R)^2xx h/H = 1/4`
`rArr (4/5)^2xxh/H = 1/4` [Using (i)]
`rArr (16/25)xx h/H=1/4`
`rArr h/H = (1xx25)/(4xx16)`
`rArr h/H = 25/64`
`therefore h: H = 25:64`
So, the ratio of their heights is 25:64.
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