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.