Hello, BobBali!

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

Therefore: .

. . . . . . . . .