The height of a cone is 20 cm. A small cone is cut off from the top by a plane parallel to the base. If its volume be 1/125 of the volume of the original cone, determine at what height above the base the section is made.
Height of the cone = 20cm
Let the small cone was cut at the height x from the top then height of the small cone = x cm
From cones ABC and AEF,
(h’, r’ and h’’, r’’ are heights and radius of larger and smaller cones resp.)
-------(i)
Given: Volume of the small cone = 
× volume of the large cone
And Volume of a cone = 
⇒ x = 4cm
Height at which section is made = 20 – 4 = 16cm
6