This question is Based on Mensuration Chapter of M.L Aggarwal book for ICSE BOARD for class 10.

Here the height of a cone is given. A small cone is cut off at the top by a plane parallel to its base. If its volume be 1/27 of the volume of the given cone, at what height above the base is the section cut?

This is the Question Number 18, Exercise 17.2 of M.L Aggarwal.

Deepak BoraNewbie

# The height of a cone is 30 cm. A small cone is cut off at the top by a plane parallel to its base. If its volume be 1/27 of the volume of the given cone, at what height above the base is the section cut?

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Given height of the cone, H = 30 cmLet R be the radius of the given cone and r be radius of small cone.Let h be the height of small cone.Volume of the given cone = (1/3)R^{2}HVolume of the small cone = 1/27 th of the volume of the given cone.(1/3)r^{2}h = (1/27)× (1/3)R^{2}HSubstitute H = 30(1/3)r^{2}h = (1/27)× (1/3)R^{2}×30r^{2}h/R^{2}= 30/27r^{2}h/R^{2}= 10/9 ….(i)From figure, r/R = h/Hr/R = h/30 ….(ii)Substitute (ii) in (i)(h/30)^{2}×h = 10/9h^{3}/900 = 10/9h^{3}= 900×10/9 = 1000Taking cube root on both sides.h = 10 cmH-h = 30-10 = 20The small cone is cut at a height of 20 cm above the base.