To find the side length of a cube given its volume, we use the formula:

$V = s^3$

where $V$ is the volume and $s$ is the side length.

Given the volume is $343 \, \text{mm}^3$, we can find the side length $s$ by taking the cube root of the volume:

$s = \sqrt[3]{343}$

Let me calculate that for you.The side length of the cube is $7.0 \, \text{mm}$.

Would you like further details or have any questions?

Here are 5 related questions to explore:

1. How would you find the surface area of this cube?
2. What would be the side length if the volume were doubled?
3. How do we calculate the diagonal length of a cube with side length 7.0 mm?
4. What is the formula for the volume of a rectangular prism, and how does it differ from that of a cube?
5. How does the volume change if the side length is doubled?

Tip: Remember that for any cube, small changes in side length result in large changes in volume since the volume scales with the cube of the side length.