The volume of a sphere of radius `2r` is

Options

A. `(32 pi r^(3))/(3)`
B. `(16 pi r^(3))/(3)`
C. `(8pi r^(3))/(3)`
D. `(64 pi r^(3))/(3)`

Answer

To find the volume of a sphere with radius \(2r\), we can follow these steps:

### Step-by-Step Solution:

1. **Recall 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. **Substitute the given radius**:
In this case, the radius is \(2r\). We will substitute \(r\) in the volume formula with \(2r\):
\[ V = \frac{4}{3} \pi (2r)^3 \]

3. **Calculate \((2r)^3\)**:
We need to calculate the cube of \(2r\):
\[ (2r)^3 = 2^3 \cdot r^3 = 8r^3 \]

4. **Substitute back into the volume formula**:
Now we can substitute \(8r^3\) back into the volume formula:
\[ V = \frac{4}{3} \pi (8r^3) \]

5. **Simplify the expression**:
Multiply \( \frac{4}{3} \) by \(8\):
\[ V = \frac{32}{3} \pi r^3 \]

### Final Answer:
The volume of the sphere with radius \(2r\) is:
\[ V = \frac{32}{3} \pi r^3 \]