Question

A cone is cut by a plane parallel to its base. The small cone on top is similar to the large cone, with a similarity ratio of 1 : 2. The ratio between the volume of the small cone to that of the frustum is

Answer 1

1 : 7

Explanation:

The ratio of the volumes is the cube of the similarity ratio:

small cone linear dimensions : large cone linear dimensions = 1 : 2

small cone volume : large cone volume = 1³ : 2³ = 1 : 8

The large cone volume is the sum of the small cone volume and frustum volume, so we have ...

small cone volume : (small cone + frustum volume) =

1 : 8 = 1 : (1+7) . . . . where "1" represents the small cone volume

Then the ratio of interests is ...

small cone volume : frustum volume = 1 : 7