Solution:
If the volume 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 25:64.Given, the ratio of volumes of two cones = 1:4.
The ratio of their diameters = 4:5.
Let r and R be the base radii of the cones.
Let h and H be the heights of the cones.
We know that, volume of the right circular cone = where r is the base radius, and h is the height of the cone.
So, the ratio of the volumes of two cones = .
Hence, the ratio of their heights = 25:64.