If the volume of two cones be in the ratio `1 : 4` and the ratii of their bases be in the ratio `4 : 5` then the ratio of their heights is

Options

A. `1 : 5`
B. `5 : 4`
C. `25 : 16`
D. `25 : 64`

Answer

D

Explanation

Let the radii of the conces be 4x cm respectively and their volume e `v cm^(3) and 4v cm^(3)` respectively. Let their heights be h cm and H cm respectively. Then,
`((1)/(3) pi xx (4x)^(2) xx h)/((1)/(3) pi xx (5x)^(2) xx H) = (v)/(4v) rArr (16h)/(25H) = (1)/(4) rArr (h)/(H) = (25)/(64)`