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A cone of radius 7 cm and slant height 15 cm was cut horizontally, resulting in a smaller cone and a frustum of a cone. If the ratio of the curved surface area of the upper and the lower part is 1 : 2, What will be the slant height of the frustum formed?

A cone of radius 7 cm and slant height 15 cm was cut horizontally, resulting in a smaller cone and a frustum of a cone. If the ratio of the curved surface area of the upper and the lower part is 1 : 2, What will be the slant height of the frustum formed? Correct Answer 15 - 5√3

Calculation:

C.S.A (small cone : frustum) = 1 : 2

∴ C.S.A (small cone : big cone) = 1 : 3

As we know, C.S.A of small cone/C.S.A of big cone = r2/R2 = l2/L2 = h2/H2

∴ slant height (small cone : big cone) = 1 : √3

A.T.Q

Slant height of big cone = 15 cm

∴ Slant height of small cone = 15/√3 = 5√3

Frustum's slant height = 15 - 5√3 cm

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