If the radius of a sphere is halved, its volume becomes______times the volume of original sphere.

Answer

To solve the problem of how the volume of a sphere changes when its radius is halved, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Volume Formula**:
The volume \( V \) of a sphere is given by the formula:
\[ V = \frac{4}{3} \pi r^3 \]
where \( r \) is the radius of the sphere.

2. **Calculate the Original Volume**:
Let the original radius of the sphere be \( r \). Therefore, the volume of the original sphere is:
\[ V_{\text{original}} = \frac{4}{3} \pi r^3 \]

3. **Determine the New Radius**:
If the radius is halved, the new radius \( R \) becomes:
\[ R = \frac{r}{2} \]

4. **Calculate the Volume of the New Sphere**:
Using the new radius \( R \), we can calculate the volume of the new sphere:
\[ V_{\text{new}} = \frac{4}{3} \pi R^3 = \frac{4}{3} \pi \left(\frac{r}{2}\right)^3 \]
Simplifying this:
\[ V_{\text{new}} = \frac{4}{3} \pi \left(\frac{r^3}{8}\right) = \frac{4}{3} \cdot \frac{\pi r^3}{8} = \frac{1}{6} \pi r^3 \]

5. **Relate the New Volume to the Original Volume**:
Now, we can express the new volume in terms of the original volume:
\[ V_{\text{new}} = \frac{1}{8} \left(\frac{4}{3} \pi r^3\right) = \frac{1}{8} V_{\text{original}} \]

6. **Conclusion**:
Therefore, the volume of the new sphere is \( \frac{1}{8} \) times the volume of the original sphere.

### Final Answer:
If the radius of a sphere is halved, its volume becomes \( \frac{1}{8} \) times the volume of the original sphere.