Question

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 smaller cone to the whole cone is

विकल्प

• A. 1 : 2

• B. 1 : 4

• C. 1 : 6

• D. 1 : 8

Answer 1

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 = 2r

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