A hollow cone is cut by a plane parallel to the base and the upper portion is removed. If the curved surface area of the remainder is 8/9th of the curved surface of the whole cone, find the ratio of the line segments into which the cone's altitude is divided by the plane.

Let *R*, *H* and *L* be the radius, height and slant height of the original cone respectively and *r*, *h* and *l* be the radius, height and slant height of the smaller cone respectively.

In ∆OAB and ∆OCD,

∠OAB = ∠OCD (90°)

∠AOB = ∠COD (Common)

∴ ∆ OAB ≅ ∆OCD (AA Similarity)

Curved surface area of the smaller cone

= Curved surface area of cone – Curved surface area of the frustum

Thus, the cones altitude is divided in the ratio 1 : 2.

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