A metallic sphere of radius 4 cm is melted and the cast into small spherical balls, each of diameter 0.4 cm. The number of small balls will be:

Options

A. 1000
B. 8000
C. 4000
D. 2000

Answer

To find the number of small spherical balls that can be made from a metallic sphere, we need to calculate the volume of the large sphere and the volume of the small balls, then divide the volume of the large sphere by the volume of one small ball.

### Step-by-Step Solution:

1. **Calculate the Volume of the Large Sphere:**
The formula for the volume \( V \) of a sphere is given by:
\[ V = \frac{4}{3} \pi r^3 \]
Here, the radius \( r \) of the large sphere is 4 cm.
\[ V_{\text{large}} = \frac{4}{3} \pi (4)^3 \]
\[ = \frac{4}{3} \pi (64) = \frac{256}{3} \pi \text{ cm}^3 \]

2. **Calculate the Volume of One Small Ball:**
The diameter of the small ball is given as 0.4 cm, so the radius \( r \) of the small ball is:
\[ r = \frac{0.4}{2} = 0.2 \text{ cm} \]
Now, using the volume formula for the small ball:
\[ V_{\text{small}} = \frac{4}{3} \pi (0.2)^3 \]
\[ = \frac{4}{3} \pi (0.008) = \frac{32}{3} \pi \text{ cm}^3 \]

3. **Calculate the Number of Small Balls:**
To find the number of small balls, we divide the volume of the large sphere by the volume of one small ball:
\[ \text{Number of small balls} = \frac{V_{\text{large}}}{V_{\text{small}}} \]
\[ = \frac{\frac{256}{3} \pi}{\frac{32}{3} \pi} \]
The \( \pi \) and \( \frac{1}{3} \) cancel out:
\[ = \frac{256}{32} = 8 \]

### Final Answer:
The number of small balls that can be made from the large metallic sphere is **8**.