If the sides of a cube are halved, its volume will become............times the original volume.

Options

A. `1//2`
B. `1//4`
C. `1//6`
D. `1//8`

Explanation

To solve the problem, we need to determine how the volume of a cube changes when its sides are halved.

### 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. **Calculate the Original Volume**:
Let the original side length of the cube be \( A \). Therefore, the original volume \( V \) is:
\[ V = A^3 \]

3. **Halve the Side Length**:
When the sides of the cube are halved, the new side length \( A' \) becomes:
\[ A' = \frac{A}{2} \]

4. **Calculate the New Volume**:
The new volume \( V' \) of the cube with the new side length \( A' \) is:
\[ V' = (A')^3 = \left(\frac{A}{2}\right)^3 \]

5. **Expand the New Volume**:
Now, calculate \( \left(\frac{A}{2}\right)^3 \):
\[ V' = \frac{A^3}{2^3} = \frac{A^3}{8} \]

6. **Relate the New Volume to the Original Volume**:
Since the original volume \( V \) is \( A^3 \), we can express the new volume in terms of the original volume:
\[ V' = \frac{A^3}{8} = \frac{V}{8} \]

7. **Conclusion**:
This means that the new volume \( V' \) is \( \frac{1}{8} \) times the original volume \( V \). Therefore, the answer is:
\[ \text{The volume will become } \frac{1}{8} \text{ times the original volume.} \]

### Final Answer:
The volume will become \( \frac{1}{8} \) times the original volume.

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