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
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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