1011:2
a hollow cone is cut by a plane parallel to the base and upper portion is removed. if the curved surface area of the remainder is 8/9 of the curved surface area of the whole cone, find the ratio of the line segments into which the cone's altitude is divided by the plane....
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4 Answers
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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 â‰
∆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.
By-Anirudh(Anidaniel)