Answer
5.7 cm
Work Step by Step
As shown in the illustration, the diameter of the smallest circle through which the box will fit is the same length as the diagonal measurement of the box. Use the Pythagorean theorem to find that length.
$a^2+b^2=c^2 \longrightarrow$ substitute the side lengths of the box
$4^2+4^2=c^2$ find the squares
$16+16=c^2 \longrightarrow$ add
$32=c^2 \longrightarrow$ find the square root of each side
$\sqrt {32}=\sqrt {c^2} \longrightarrow$ simplify
$5.7=c$
