Geomety-5

A cone of radius 4 cm with a slant height of 12 cm was sliced horizontally, resulting into a smaller cone (upper portion) and a frustum (lower portion). If the ratio of the curved surface area of the upper smaller cone and the lower frustum is 1:2, what will be the slant height of the frustum?

(A) 12 – √3
(B) 12 – 2√3
(C) 12 – 3√3
(D) 12 – 4√3
(E) None of the above














SOLUTION:

The curved surface area of the small cone and the frustum are in the ratio 1:2
Therefore, CSA of the smaller and the bigger cone are in the ratio 1:3
Hence, the linear dimension will be in the ratio 1:√3
The slant height of the bigger cone is 12, hence for the small cone it would be 4√3
Hence we conclude that for the frustum it would be 12-4√3
Hence option D is the correct choice.

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