1. A solid right circular cone is cut into two parts at the middle of its height by a plane parallel to its base . The ratio of the volume of the small cone isto whole cone is : ?

Let the height and the radius of whole cone be *H *and *R *respectively.

The cone is divided into two parts by drawing a plane through the mid point of its height and parallel to the base.

Let the radius of the smaller cone be *r* cm.

In ∆OCD and ∆OAB,

∠OCD = ∠OAB (90°)

∠COD = ∠AOB (Common)

∴∆OCD ∼ ∆OAB (AA Similarity criterion)

⇒ *R* = 2*r*

Thus, the ratio of smaller cone to whole cone is 1 : 8.

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