If the volume of two right circular cones are in the ratio 4 : 1 and their diameter are in the ratio 5 : 4, then the ratio of their height is:

64 : 25

Volume :       4    :    1

Radius:         5    :    4               (ratio of diameter = ratio of radius)

Radius² :      25   :    16   

Ratio of height =  \(\frac{Vol._1}{R^2}\)  :  \(\frac{Vol._2}{r^2}\)

Height :      \(\frac{4}{25}\)  :  \(\frac{1}{16}\) = 64   :    25