Optimisation: An ornamental container consists of a cuboid-shaped hole inside a sphere.

[lookagain]

It is a negative sign, therefore indicating it is a maximum (3*2R/sqrt(3)), which I believe would be equal to -6R/sqrt(3)?

Is the maximum value 8R^3/3sqrt(3) cm^3 ?

The value of the second derivative is -6R/sqrt(3).

The maximum value of the volume is 8R^3/[3sqrt(3)] cm^3. \(\displaystyle \ \ \) You need some type of additional grouping
symbols in the denominator when writing this in horizontal style due to the Order of Operations.

We could also rationalize the denominator and write the fraction with the radical in the numerator instead.