Q. 21

# A solid right cir

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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