find the dimentions of a bose of largest area that can be inscribed in a sphere of radius 1
I will assume you meant:
"largest volume"
Obviously the "bose" must be a cube.
Sketch a cross-section
I see a square in a circle, with a diameter of 2.
let each side of the cube be x
then x^2 + x^2 = 2^2
2x^2 = 4
x^2 = 2
x = √2
The "bose" is √2 on all sides
btw, it is dimensions, not "dimentions"