How many spherical bullets can be made out of a solid cube of lead whose edge measures 44 cm, each bullet being 4 cm in diameter.

Answer

To find out how many spherical bullets can be made from a solid cube of lead, we will follow these steps:

### Step 1: Calculate the Volume of the Cube
The volume \( V \) of a cube is given by the formula:
\[ V = a^3 \]
where \( a \) is the length of an edge of the cube. Here, the edge of the cube measures 44 cm.

\[ V = 44^3 = 44 \times 44 \times 44 \]
Calculating \( 44^3 \):
\[ 44 \times 44 = 1936 \]
\[ 1936 \times 44 = 85384 \text{ cm}^3 \]

### Step 2: Calculate the Volume of One Bullet
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. The diameter of each bullet is 4 cm, so the radius \( r \) is:
\[ r = \frac{4}{2} = 2 \text{ cm} \]
Now, substituting \( r \) into the volume formula:
\[ V = \frac{4}{3} \pi (2)^3 = \frac{4}{3} \pi (8) = \frac{32}{3} \pi \text{ cm}^3 \]
Using \( \pi \approx \frac{22}{7} \):
\[ V \approx \frac{32}{3} \times \frac{22}{7} = \frac{704}{21} \text{ cm}^3 \]

### Step 3: Calculate the Number of Bullets
Let \( n \) be the number of bullets that can be made. The total volume of the bullets must equal the volume of the cube:
\[ n \times \text{Volume of one bullet} = \text{Volume of the cube} \]
\[ n \times \frac{32}{3} \pi = 85384 \]
Substituting \( \pi \) with \( \frac{22}{7} \):
\[ n \times \frac{32}{3} \times \frac{22}{7} = 85384 \]
\[ n \times \frac{704}{21} = 85384 \]
Now, solve for \( n \):
\[ n = \frac{85384 \times 21}{704} \]
Calculating the right side:
\[ n = \frac{1790544}{704} = 2544 \]

### Final Answer
Thus, the number of spherical bullets that can be made from the solid cube of lead is:
\[ \boxed{2544} \]