If the volumes of two cones are in ratio 1:4 and their diametres are in the ratio 4:5, find the ratio of their heights.
Let v1 & v2 be volume of two cnes.
Given v1v2=14 ------- (1)
Let d1 & d2 be diameters of cones
d1d2=45
From equation (1)
13π(D12)2h113π(D12)2h2=14
h1h2=14×D22(D1)2=14(D2D1)2
h1h2=14×(54)2=2564
∴ ratio of heights of cone is 25:64.