Question

If the volumes of two cones are in the ratio 1 : 4 and their diameters are in the ratio 4 : 5, then write the ratio of their heights.

Answer 1

Answer:

The ratio of their heights is  25 : 64.

Step-by-step explanation:

Given :  

Volume of the two cones = V1 : V2 = 1 : 4 and diameter of the two cones = d1 : d2 = 4 : 5

Let the Radius be r1 & r2 & height be h1 & h2 of two cones

d1/d2 = ⅘

2r1/2r2 = ⅘

r1/r2 = ⅘ ……………(1)

V1/V2 = (1/3πr1² h1) / (1/3πr2² h2)

[Volume of cone = ⅓ πr²h]  

¼ = r1²h1/r2²h2

¼ =  (r1 /r2 )² ×  (h1 /h2)

¼ = ( 4/5 )² × (h1 / h2)

[From eq 1]

¼ = 16/25 × h1/h2

h1/h2 = ¼ × 25/16

h1/h2 =  25/64

h1: h2 =  25: /64

Hence, the ratio of their heights is  25 : 64.

HOPE THIS ANSWER WILL HELP YOU ..

Answer 2

Refer to the attachment .