Q. 5 3.9( 12 Votes )

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 :

Let V1 be the volume of first cone and V2 be the volume of second cone.

Then, V1:V2 = 1:4

Let d1 be the diameter of first cone and d2 be the diameter of second cone.

Then d1:d2 = 4:5

Let h1 be the height of first cone and h2 be the height of second cone.

We know that volume of cone is given by V = 1/3 × π(d2/4)h

h1:h2 = 25:64

Ratio of height of two cones is 25:64.

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