A spherical ball of lead has been melted and meade in to smaller balls of half the radius of the original one. How many balls can be made?

Answer

To solve the problem of how many smaller balls can be made from a larger spherical ball of lead, we will follow these steps:

### Step-by-Step Solution:

1. **Identify the radius of the original ball**:
Let the radius of the original spherical ball be \( r \).

2. **Calculate the volume of the original ball**:
The volume \( V_1 \) of a sphere is given by the formula:
\[ V_1 = \frac{4}{3} \pi r^3 \]

3. **Identify the radius of the smaller balls**:
The radius of each smaller ball is half of the original radius, so:
\[ \text{Radius of smaller ball} = \frac{r}{2} \]

4. **Calculate the volume of one smaller ball**:
The volume \( V_2 \) of a smaller ball is given by the formula:
\[ V_2 = \frac{4}{3} \pi \left(\frac{r}{2}\right)^3 \]
Simplifying this:
\[ V_2 = \frac{4}{3} \pi \left(\frac{r^3}{8}\right) = \frac{4}{24} \pi r^3 = \frac{1}{6} \pi r^3 \]

5. **Determine how many smaller balls can be made**:
To find the number of smaller balls that can be made from the original ball, divide the volume of the original ball by the volume of one smaller ball:
\[ \text{Number of balls} = \frac{V_1}{V_2} = \frac{\frac{4}{3} \pi r^3}{\frac{1}{6} \pi r^3} \]
The \( \pi r^3 \) terms cancel out:
\[ \text{Number of balls} = \frac{\frac{4}{3}}{\frac{1}{6}} = \frac{4}{3} \times 6 = 8 \]

### Conclusion:
Thus, the number of smaller balls that can be made is **8**.