Right circular cone containing a sphere (optimization)

[ZyzzBrah]

Determine the dimensions of a right circular cone (radius and height) containing a sphere of radius a. if the volume of the cone is to be minimum.


i have no edea where to start
but frst i need to know if the sphere is inscribed inside a cone

and the volumes of the two how do i relate? what volume to differentiate and its parameters to get the minimum possible volume of the cone

 

[tkhunny]

"containing" is important. I believe the sphere mustn't stick out.

The sphere will touch the cone in a circle. Spheres and circles have constant radius.

That's enough to start. Let's see where it leads you.

 

[renegade05]

Cough*cough* similar triangles * cough*cough*