The length of each edge of a cube was made 5 times larger.How much larger did the volume become?

1. Break Down the Problem

To determine how much larger the volume of a cube becomes when each edge length is increased by a factor of 5, we need to calculate the initial volume and the new volume after the changes.

2. Relevant Concepts

The volume $V$ of a cube is given by the formula: $V = s^3$ where $s$ is the length of an edge of the cube.

3. Analysis and Detail

• Initial Volume: Let the initial edge length be $s$. The volume of the cube is: $V_{\text{initial}} = s^3$

• New Volume: After increasing the edge length by 5 times, the new edge length becomes $5s$. The new volume is: $V_{\text{new}} = (5s)^3$ Calculating the new volume: $V_{\text{new}} = 125s^3$

4. Verify and Summarize

Now, to find how much larger the volume has become, we can compute the ratio of the new volume to the initial volume: $\text{Increase in Volume} = \frac{V_{\text{new}}}{V_{\text{initial}}} = \frac{125s^3}{s^3} = 125$ This implies that the volume has increased 125 times compared to the original volume.

Final Answer

The volume of the cube became 125 times larger after increasing the length of each edge by a factor of 5.