A cube measuring 5 cm on each side is made from 125 equal cubes.What is the volume of one of the small cubes?

1. Break Down the Problem

To find the volume of one of the smaller cubes, we first need to determine the volume of the larger cube and then divide that by the number of smaller cubes.

2. Relevant Concepts

The volume $V$ of a cube is calculated using the formula: $V = s^3$ where $s$ is the length of a side of the cube.

3. Analysis and Detail

1. Calculate the volume of the larger cube:

   • The side length of the larger cube is $5 \, \text{cm}$.
   • Therefore, the volume of the larger cube is: $V_{\text{large}} = (5 \, \text{cm})^3 = 125 \, \text{cm}^3$

2. Determine the volume of one smaller cube:

   • The larger cube is made up of 125 equal smaller cubes.
   • Thus, the volume of one smaller cube is: $V_{\text{small}} = \frac{V_{\text{large}}}{\text{Number of smaller cubes}} = \frac{125 \, \text{cm}^3}{125} = 1 \, \text{cm}^3$

4. Verify and Summarize

The calculations show that the volumes were derived correctly, and dividing the total volume by the number of smaller cubes yields the individual volume accurately.

Final Answer

The volume of one of the small cubes is $1 \, \text{cm}^3$.