Answer:
4 inches on each edge of the cube
Explanation:
A closed box will have minimum area when it is a cube. For a volume of 64 in^3, the edge length must be ∛64 = 4 inches.
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Using derivatives, the base edge length can be defined as x, and the surface area as ...
S = 2x^2 + 4x(64/x^2)
This is minimized when dS/dx = 0:
dS/dx =- 4x -256/x^2 = 0
x^3 = 64
x = ∛64 = 4 . . . . . should look familiar