a parallel to base divides a cone in two parts of equal volume , determine the ratio of the heights of the two parts that is the cone and the frustum..??
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Volume of the cone = [= 1(
Since the volume is divided equally, volume of the smaller cone = [1(
= 1(
Both the cones formed are similiar so using the identity for similiar figures
V1/V2 = (L1/L2)³
Since the ratio of volumes is 1:2
1/2 = (L1/L2)³
1/(∛2) = (L1/L2)
This is the ratio of any of the length of the similiar shapes so the ratio of the smaller cone and the frustum is:
1 : (∛2 - 1)