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

volume of cone=1/3*pie*r^2h
ratio r^2h/R^2H=1/4
16*h/25*H=1/4
h/H=25/64
radio of height=25:64

Answer 2

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】