Find the dimensions of the rectangular box with the largest volume if the total surface area is given as 64 cm^2.

Answer 1

Insufficient data.
Is there a top to the box
Is the base a square?

If so, then all sides must be equal,
let each side be x cm long
so you have 6x^2 = 64
x = 8/√6 or 8√6/6 = 4√6/3 cm

Then the largest volume = (4√6/3)^3 = approx 34.84 cm^3