Question

The radius of the base of a right circular cone is 6 and the radius of a parallel cross section is 4. If the distance between the base and the cross section is 8, what is the height of the cone?

A. 11
B. 13 1/3
C. 16
D. 20
E. 24

Answer 1

[see the figure attached]
Let's take a look at a vertical section of the cone.
By Thales' theorem, the height is
`(BD)/(CE)=(AB)/(AC)` hence
`h=AC=(AB\cdot CE)/(BD)=((h-8)\cdot6)/(4)` thus
`\boxed{h=24}`

Answer E