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

Answer

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

### Step-by-Step Solution:

1. **Define the Initial Edge Length:**
Let the edge length of the initial cube be \( A \).

2. **Calculate the Initial Surface Area:**
The formula for the surface area \( S \) of a cube is given by:
\[ S = 6A^2 \]
So, the initial surface area \( S \) is:
\[ S = 6A^2 \]

3. **Determine the New Edge Length:**
If each edge of the cube is doubled, the new edge length becomes:
\[ 2A \]

4. **Calculate the New Surface Area:**
Using the new edge length, the surface area \( S' \) of the new cube is:
\[ S' = 6(2A)^2 \]
Simplifying this, we get:
\[ S' = 6 \times 4A^2 = 24A^2 \]

5. **Compare the New Surface Area to the Initial Surface Area:**
Now, we need to find out how many times the new surface area \( S' \) is compared to the initial surface area \( S \):
\[ \text{Increase Factor} = \frac{S'}{S} = \frac{24A^2}{6A^2} \]
Simplifying this gives:
\[ \text{Increase Factor} = \frac{24}{6} = 4 \]

### Conclusion:
The surface area of the cube increases by a factor of **4** when each edge is doubled.

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