Actually, this is not a max-min calculus problem at all!
A 20 cm nail fits inside a cylindrical can.
Find the maximum radius of 3 identical balls that will fit exactly inside the can?
I have drawn the diagram to the best of my ability.
I thought the nail is lying diagonally (AB) and I split the diag to make right triangles.
*h = Radius
. These two equations are equivalent!
Consider the largest right triangle.
The height is
The base is
The hypotenuse is
. . . . . . . . .