If each side of a cube is doubled then its volume

Options

A. is doubled
B. becomes 4 times
C. becomes 6 times
D. becomes 8 times

Explanation

To solve the problem of finding the new volume of a cube when each side is doubled, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Volume of a Cube**:
The volume \( V \) of a cube with side length \( A \) is given by the formula:
\[ V = A^3 \]

2. **Double the Side Length**:
If each side of the cube is doubled, the new side length becomes \( 2A \).

3. **Calculate the New Volume**:
Now, we need to find the volume of the new cube with side length \( 2A \):
\[ V' = (2A)^3 \]

4. **Expand the New Volume**:
Using the property of exponents, we can expand this:
\[ V' = 2^3 \times A^3 = 8A^3 \]

5. **Compare the New Volume with the Old Volume**:
The original volume was \( A^3 \). The new volume is \( 8A^3 \). Therefore, the new volume is:
\[ V' = 8 \times V \]
This means the new volume is 8 times the original volume.

### Final Answer:
If each side of a cube is doubled, its volume becomes 8 times the original volume.