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The height of a cone is 30 cm . a small cone is cut off at the top by a plane parallel to the base if its volume be 1/27 of the volume of the given cone,at

what height above the base is the section mode.



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Volume of the big cone = V =  π/3 * R² H
           H = 30 cm

Volume of the small cone , which is cut off = π/3 r² h

In the regular cone, the radius of the base circle and the height increase proportionately from the apex.    Hence  r = R/x    and  h = H/x,    where x = a positive number

     Volume of small cone = π/3 R²H/x³ = V/x³ = 1/27 * V
                   => x = 3
Hence height of small cone = H/3 = 10 cm
Height of the remaining part of cone = 20 cm

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