I was working on Lagrange Multipliers but I want to find another method using Geometry..
From calculus book the question is, with the information given,
"Find the dimensions of the rectangular box of maximum volume that can be inscribed inside the sphere $x^2 +y^2 +z^2 = 4$"
I understand how to do it their way and I do not seek an optimization approach or a Lagrange Multiplier approach but a geometric one with shapes/triangles and algebra and reason behind the process.
The answer is that the volume consists of all like edges, $\frac{4}{\sqrt{3}}$ and I can work backwards geometrically from this answer given in the book but I want to know if you can work forward from the information given only by the initial problem using geometry.