If the volumes of two cones are in the ratio 1:4 and their diameters are in the ratio 4:5, then the ratio of their heights, is

Answer

`25:64`

Explanation

Let the radii of the cones be 4r and 5r and their heghts be `h_(1)" and "h_(2)` respectively. Then,
`(1/3pixx(4r)^(2)xxh_(1))/(1/3pixx(5r)^(2)xxh_(1))=1/4rArr(16h_(1))/(25h_(2))=1/4rArrh_(1)/h_(2)=1/4xx25/16=25/64`