Question

if the volumes of two cones are in the ratio of 1:4 and their diameters are in the ratio of 4:5 find the ratio of their heights​

Answer 1

Answer:

Step-by-step explanation:

here, given Volume of the two cones = 1 :4

and diameter = 4 : 5

then , find ratio of height ???

now,

the solution:-

v1/v2 = 1/3πr1² h1 / 1/3πr2² h2 = 1/ 4.............【1】

d1/d2 = 2r1/ 2r2 = 4 / 5........................【2】

now, by simplifying eqn 【1】as

( r1 /r2 )² h1 /h2 = 1/ 4

now, similarly by using eqn【2】we get the result,

( 4/5 )² × h1 / h2 = 1/ 4

so, h1 / h2 = 1 /4 × 25/ 16

therefore, h1/ h2 = 25 / 64

therefore , we can say ratio of their heights = 25 : 64 【ans】

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Answer 2

Answer:

25:64

Step-by-step explanation:

Let h1 and h2 are the heights for volume v1 and v2 then writing equation for h1 and h2 and dividing, we get-

v1/v2= (d1/d2)^2* (h1/h2)

1/4=(4/5)^2*(h1/h2)

1/4=16/25*(h1/h2)

Therefore(h1/h2)=25/64

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