XAT 2018 Geometry & Mensuration Question (Medium)

Question

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?

Optima Learn · Accepted Answer

Let the smaller cone have slant height l and radius r. By similarity, 4 12 Rightarrow r 3 . Curved surface area CSA of the small cone is pi r l. CSA of the frustum is pi 4 r 12-l . Given pi 4 r 12-l 2 , substitute r 3 3 left 4 3 right 12-l 2 . This gives 2l 2 12 l 12-l 144-l 2 Rightarrow 3l 2 144 Ri

XAT 2018 Geometry & Mensuration — Previous Year Question

XAT 2018

Quantitative

Geometry & Mensuration

Medium

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