Volume of cone : (πr²h)/3

Where r= radius of cone and h = height of cone.

Let V1 be the volume of one cone and V2 the other.

Then V1=(π(r1)² h1)/3

V2=(π [r2]² h2)/3

V1:V2=1:4

V2=4V1. This leads to

(π/3)(r2)² h2=4*(π/3)(r1)² h1

Simplifying the equation ,we have

(r2)² *h2=4*(r1)² *h1…1

Also the diameters are in the ratio 4:5.

So r1:r2=4:5

4r2=5r1

r2=(5/4)r1

Substituting these in equation 1

{(5/4)r1}² * h2=4*(r1)² * h1

(25/16) * h2 = h1 * 4

25 h2 = 4 * 16h1

25 h2 = 64h1

h1:h2=25:64

The heights are in the ratio 25:64