Find the approximate volume of metal in a hollow spherical shell whose internal and external radii are 3 cm and 3.0005 cm, respectively.

Explanation

To find the approximate volume of metal in a hollow spherical shell with internal radius \( r_1 = 3 \) cm and external radius \( r_2 = 3.0005 \) cm, we can use the formula for the volume of a sphere and the concept of differentiation to estimate the change in volume due to a small change in radius.

### Step-by-Step Solution:

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