Calculate Cube Edge Length from Volume: 125 cm³ Problem

To solve this problem, we will follow these steps:

• Step 1: Identify the given information.
• Step 2: Apply the appropriate formula.
• Step 3: Perform the necessary calculations to determine the length of the edge.

Now, let's work through each step:
Step 1: The problem gives us the volume of the cube as $125 \, \text{cm}^3$.
Step 2: The formula for the volume of a cube is $V = a^3$, where $a$ is the length of a side of the cube.
Step 3: We substitute the given volume into the formula: $125 = a^3$. Solving for $a$, take the cube root of both sides:

$a = \sqrt[3]{125}$

Recognizing $125$ as a perfect cube, we have $125 = 5^3$. Therefore,

$a = 5 \, \text{cm}$

Thus, the length of each edge of the cube is $5 \, \text{cm}$.

This matches the correct choice from the multiple options provided, confirming our calculations.

The solution to the problem is $a = 5 \, \text{cm}$.