What is the side of a cube (in metres) in which an iron rod of maximum length $10\text{ metres}$ can be put?

The longest rod that can fit inside a cube corresponds to the body diagonal of the cube.The formula for the body diagonal of a cube with side length $a$ is given by:
$$\text{Diagonal}=a\sqrt{3}$$
Given that the maximum length of the rod is $10\text{ metres}$:
$$a\sqrt{3}=10$$
$$a=\frac{10}{\sqrt{3}}$$
Since $\sqrt{3}\approx 1.732$:
$$a=\frac{10}{1.732}\approx 5.7735\text{ metres}$$
Rounding off to two decimal places, the side of the cube is $5.77\text{ metres}$.