Question

The height of a cone is 30 cm. A small cone is cut off at the top by a plane parallel to its base. If its volume be `1/27` of the volume of the given cone, at what height above the base is the section cut? 

Answer 1

Given:

Height of the given cone,

H = 30 cm

Volume of the small cone

`= 1/27 xx` (volume of the given cone)

Since the cutting plane is parallel to the base the two cones are similar.

`"Volume of small cone"/"Volume of big cone" = (h/H)^3`

`1/27 = (h/30)^3`

Taking cube root on both sides: 

`1/3 = h/30`

h = 10 cm

Height of section above the base: = 30 − 10 = 20 cm

The section is cut at a height of 20 cm above the base.