The volume of a cube is 125 cm³. What is the length of one side of the cube?A. 5 cmB. 10 cmC. 15 cmD. 25 cm

1. Break Down the Problem

To find the length of one side of the cube, we need to use the formula for the volume of a cube, which is: $V = s^3$ where $V$ is the volume and $s$ is the length of one side.

2. Relevant Concepts

Given the volume $V = 125 \, \text{cm}^3$, we need to solve for $s$: $s = V^{1/3}$

3. Analysis and Detail

Now, we can calculate the length of one side: $s = 125^{1/3}$ To find $125^{1/3}$, we can recognize that $125 = 5^3$: $s = (5^3)^{1/3} = 5$

4. Verify and Summarize

We have calculated $s$ to be $5$ cm. To verify: $V = s^3 = 5^3 = 125 \, \text{cm}^3$ This matches the given volume.

Final Answer

The length of one side of the cube is 5 cm (Option A).