A small cone of height 8 cm is cut off from a bigger cone to leave a frustum of height 16 cm. If the volume of the smaller cone is 160 cubic centimeter find the volume of the frustum

Answer 1

Draw a cross-section of the cone
The height of the whole original cone is 24 cm

the volumes of similar solids are proportional to the cube of their corresponding sides, so ...

volume_whole/160 = 24^3/8^3 = 27

volume_whole = 160(27) = .... cm^3

so volume of frustum = volume_whole - 160 cm^3
= .....

or, the long way:
find the radius r of the small cone which was cut off
(1/3)π(8)r^2 = 160
r = ...
let the radius of the large (original) cone be R
by ratios:
R/r = 24/8 = 3
R = 3r = ...

Now find the volume of each of the cones
frustum = volume of large cone - volume of small cone

(I got the same answer)