From a given solid cone of height H, another inverted cone is carved whose height is h such that its volume is maximum. Then the ratio `H/h` is

Answer

3

Explanation

`r=R(H-h)/(H)`
`volume (V)=1/3 pi (R^(2))(H-g)^(2)/(H^(2)).h=(piR^(2))/(3H^(2))(H-h)^(2)h`
`therefore (dv)/(dh)=(piR^(2))/(3H^(2))[(H-h)^(2)-2h(H-h)]`
`=(piR^(2))/((3H^(2))(H-h)(H-h-2h)`
Therefore `(dv)/(dh)=0 if h=(H)/(3)`
Also `h=(H)/(3)` is a point of maxima thus `(H)/(h)=3`