the volumes of the 2 cones are in the ratio 1:4 and their diameters are in the ratio 4:5. find the ratio of their heights ?

let volumes of cones are v11 & v2 & DIAMETERS ARE d1 & d2 & LET HEIGHTS BE H1 & H2
v1/v2= 1/4 ------------------(i)
d1/d2= 4/5---------------(ii)
NOW V1= 1/3pi (d1/2)^2h1 & v2= 1/3pi(d2/2)^2 h2
so dividing v1/v2=( d1)^2h1/(d2)^2h2 =1/4
or (4/5)^2h1/h2 = 1/4
or h1/h2= 25/64
so ratio of heights is 25 : 64

1V = Pi(4x)^2(H1)
4V= Pi(5x)^2(H2)
1/4 = (16/25)(H1/H2)
H1/H2 = 25/64
Ratio is 25:64

Va = (1/4)Vb, Ra = (4/5)Rb.
Va = (1/3)pi*(Ra)^2*Ha,
Vb = (1/3)pi*(Rb)^2*Hb =>
Va/Vb = [Ra/Rb]^2*(Ha/Hb) =>
Ha/Hb = (1/4)/(4/5)^2 = 25/64.
Answer is 25:64.