This problem involves finding the value of $z$, the side length of a cube, given its volume. The formula for the volume of a cube is:

$V = z^3$

Given:

$V = 125 \, \text{cubic feet}$

Step-by-step Solution:

1. Substitute $V = 125$ into the formula: $125 = z^3$

2. Solve for $z$ by taking the cube root of both sides: $z = \sqrt[3]{125}$

3. The cube root of 125 is: $z = 5$

Thus, the side length $z$ is $\mathbf{5 \, \text{ft}}$.

Answer:

The value of $z$ is $\mathbf{5 \, \text{ft}}$.

Would you like further details or explanations?

Here are 5 related questions for practice:

1. What is the volume of a cube with a side length of 4 ft?
2. If the volume of a cube is 343 cubic feet, what is the side length?
3. How does the formula for the volume of a rectangular prism differ from that of a cube?
4. If the side length of a cube doubles, how does its volume change?
5. How can you approximate the cube root of a non-perfect cube?

Tip: To solve cube root problems efficiently, memorize the cubes of small integers (e.g., $2^3 = 8$, $3^3 = 27$, etc.).