If each edge of a cube is doubled,
how many times will its volume increase?

Answer

To solve the problem of how many times the volume of a cube increases when each edge is doubled, we can follow these steps:

### Step-by-Step Solution:

1. **Define the side length of the original cube**:
Let the side length of the original cube be \( a \).

2. **Calculate the volume of the original cube**:
The volume \( V \) of a cube is given by the formula:
\[ V = a^3 \]
So, the volume of the original cube is:
\[ V = a^3 \]

3. **Determine the new side length after doubling**:
If each edge of the cube is doubled, the new side length becomes:
\[ 2a \]

4. **Calculate the volume of the new cube**:
Using the new side length, the volume \( V' \) of the new cube is:
\[ V' = (2a)^3 \]
Expanding this, we get:
\[ V' = 2^3 \cdot a^3 = 8a^3 \]

5. **Compare the volumes**:
Now, we compare the volume of the new cube \( V' \) with the volume of the original cube \( V \):
\[ V' = 8a^3 \]
Since the original volume \( V = a^3 \), we can express the relationship as:
\[ V' = 8 \times V \]

6. **Conclusion**:
Therefore, the volume of the cube increases by a factor of 8 when each edge is doubled.

### Final Answer:
The volume of the cube increases 8 times.

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