Answer :


Given: A solid right circular cone is cut into two parts at the middle of its height by a plane parallel to its base


Let ‘H’ be the height of the cone.


Let ‘R’ be the Radius of the complete cone.


Volume of a cone is given by: πr2h


Here,


AB = BD =


Let r be the radius of the smaller cone.


In ΔABC and ΔADE


ABC = ADE (90°)


CAB = EAB (common)


ΔABC ΔADE (AA similarity criterion)


= (Corresponding sides are proportional)


=


R = 2r


Volume of smaller cone = π(r)2 × h = π(BC)2 × AB = π(r)2 × = cm3


Volume of whole cone = π(r)2 × h = π(DE)2 × AD = π(2r)2 × H = πr2H cm3


= =


The ratio of the volume of the smaller cone to the whole cone is 1:8

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