If the radius of a sphere is doubled, its volume becomes _______ times the volume of original sphere.

Answer

To solve the problem of how many times the volume of a sphere increases when its radius is doubled, follow these steps:

### Step-by-Step Solution:

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

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

3. **Determine the new radius when it is doubled**:
If the radius is doubled, the new radius \( R \) becomes:
\[ R = 2r \]

4. **Calculate the volume of the new sphere**:
Using the new radius \( R \), the volume of the new sphere is:
\[ V_{\text{new}} = \frac{4}{3} \pi R^3 = \frac{4}{3} \pi (2r)^3 \]

5. **Simplify the volume of the new sphere**:
Calculate \( (2r)^3 \):
\[ (2r)^3 = 8r^3 \]
Thus, the volume of the new sphere becomes:
\[ V_{\text{new}} = \frac{4}{3} \pi (8r^3) = \frac{32}{3} \pi r^3 \]

6. **Relate the new volume to the original volume**:
We can express the new volume in terms of the original volume:
\[ V_{\text{new}} = 8 \left( \frac{4}{3} \pi r^3 \right) = 8 V_{\text{original}} \]

7. **Conclusion**:
Therefore, if the radius of a sphere is doubled, its volume becomes **8 times** the volume of the original sphere.