If the radius of a sphere becomes 3 times then how many times will its volume be?

Answer

To solve the problem of how many times the volume of a sphere increases when its radius is tripled, 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. **Define the Original Radius**:
Let the original radius of the sphere be \( r \).

3. **Calculate the Original Volume**:
Using the formula for volume, the original volume \( V \) can be expressed as:
\[ V = \frac{4}{3} \pi r^3 \]

4. **Determine the New Radius**:
If the radius becomes 3 times the original radius, the new radius \( R \) is:
\[ R = 3r \]

5. **Calculate the New Volume**:
Substitute the new radius into the volume formula to find the new volume \( V' \):
\[ V' = \frac{4}{3} \pi R^3 = \frac{4}{3} \pi (3r)^3 \]

6. **Simplify the New Volume**:
Now, simplify \( (3r)^3 \):
\[ (3r)^3 = 27r^3 \]
Therefore, the new volume becomes:
\[ V' = \frac{4}{3} \pi (27r^3) = 27 \left(\frac{4}{3} \pi r^3\right) \]
This means:
\[ V' = 27V \]

7. **Conclusion**:
The new volume \( V' \) is 27 times the original volume \( V \). Thus, when the radius of the sphere is tripled, its volume increases by a factor of 27.

### Final Answer:
The volume of the sphere becomes **27 times** the original volume.

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