Maximize Volume of Right Circular Cone with Constant Slant Edge

[disfused_3289]

1. The slant edge of a right circular cone is 6 cm in length. Find the height of the cone when the volume is a maximum.

2. Find the maximum volume of a right circular cone whose slant edge has a constant length measure a.

 

[dodo]

I would add,
3. Express the volume V(x) of a right circular cone in terms of the length x of its slant edge.

Then solve 3, then 2, then 1.