How many bullets can be made from a sphere of 8 cm radius . The radius of each bullet must be 0.2 cm.

Answer

To find out how many bullets can be made from a sphere with a radius of 8 cm, where each bullet has a radius of 0.2 cm, we will follow these steps:

### Step 1: Calculate the volume of the 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 sphere is 8 cm.

Substituting the value into the formula:

\[ V = \frac{4}{3} \pi (8)^3 \]

Calculating \( (8)^3 \):

\[ (8)^3 = 512 \]

Now substituting back:

\[ V = \frac{4}{3} \pi (512) = \frac{2048}{3} \pi \, \text{cm}^3 \]

### Step 2: Calculate the volume of one bullet
The formula for the volume \( V \) of a hemisphere (since bullets are typically modeled as hemispheres) is given by:

\[ V = \frac{2}{3} \pi r^3 \]

Here, the radius \( r \) of each bullet is 0.2 cm.

Substituting the value into the formula:

\[ V = \frac{2}{3} \pi (0.2)^3 \]

Calculating \( (0.2)^3 \):

\[ (0.2)^3 = 0.008 \]

Now substituting back:

\[ V = \frac{2}{3} \pi (0.008) = \frac{0.016}{3} \pi \, \text{cm}^3 \]

### Step 3: Set up the equation to find the number of bullets
Let \( n \) be the number of bullets. The total volume of the bullets must equal the volume of the sphere:

\[ n \times \frac{2}{3} \pi (0.2)^3 = \frac{4}{3} \pi (8)^3 \]

Substituting the volumes we calculated:

\[ n \times \frac{0.016}{3} \pi = \frac{2048}{3} \pi \]

### Step 4: Cancel out \( \pi \) and solve for \( n \)
Dividing both sides by \( \pi \):

\[ n \times \frac{0.016}{3} = \frac{2048}{3} \]

Now, multiply both sides by 3 to eliminate the fraction:

\[ n \times 0.016 = 2048 \]

Now, divide both sides by 0.016 to solve for \( n \):

\[ n = \frac{2048}{0.016} \]

Calculating \( n \):

\[ n = 128000 \]

### Conclusion
Thus, the number of bullets that can be made from the sphere is **128000**.

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