The question asks to determine the side length $z$ of a cube given its volume, which is $125 \, \text{cubic feet}$.

The formula for the volume of a cube is:

$V = z^3$

Given $V = 125$, solve for $z$:

$z^3 = 125$

Taking the cube root of both sides:

$z = \sqrt[3]{125} = 5$

Thus, the value of $z$ is 5 feet.

Would you like further explanation or related examples? Here are five questions related to this concept:

1. What is the formula for the surface area of a cube with a side length of $z$?
2. If the volume of a cube is $64 \, \text{cubic units}$, what is the side length?
3. How does the formula for the volume of a rectangular prism differ from that of a cube?
4. What would happen to the volume if the side length of the cube doubles?
5. Can a cube with a volume of $27 \, \text{cubic meters}$ have a side length that is not an integer?

Tip: Always check that the volume corresponds to the cube of an integer to quickly estimate the side length without a calculator.