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 = 2r

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

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1 : 8

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let the height of small cone be h, then height of large cone is 2h. Let the radius of smaller cone be r. Then the radius of larger cone is 2r.

now ratio is = 1/3pie r2h/1/3pie(2r)22h.

  =>  r2h/4r22h

=>  1:8

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