To find the number of spherical lead shots that can be made from a solid cuboid of lead, we will follow these steps:
### Step 1: Calculate the volume of the cuboid
The volume \( V \) of a cuboid is given by the formula:
\[
V = \text{length} \times \text{breadth} \times \text{height}
\]
For the given dimensions of the cuboid (24 cm, 22 cm, and 12 cm):
\[
V = 24 \, \text{cm} \times 22 \, \text{cm} \times 12 \, \text{cm}
\]
### Step 2: Compute the volume of the cuboid
Calculating the above expression:
\[
V = 24 \times 22 \times 12 = 6336 \, \text{cm}^3
\]
### Step 3: Calculate the volume of one spherical lead shot
The volume \( V \) of a sphere is given by the formula:
\[
V = \frac{4}{3} \pi r^3
\]
First, we need to find the radius \( r \) of the spherical lead shot. The diameter is given as 6 cm, so:
\[
r = \frac{\text{diameter}}{2} = \frac{6 \, \text{cm}}{2} = 3 \, \text{cm}
\]
Now, substituting \( r \) into the volume formula:
\[
V = \frac{4}{3} \pi (3 \, \text{cm})^3
\]
### Step 4: Compute the volume of one spherical lead shot
Calculating the volume:
\[
V = \frac{4}{3} \pi (27) = 36 \pi \, \text{cm}^3
\]
Using \( \pi \approx 3.14 \):
\[
V \approx 36 \times 3.14 = 113.04 \, \text{cm}^3
\]
### Step 5: Calculate the number of spherical lead shots
To find the number of spherical lead shots, we divide the volume of the cuboid by the volume of one spherical lead shot:
\[
\text{Number of shots} = \frac{\text{Volume of cuboid}}{\text{Volume of one shot}} = \frac{6336 \, \text{cm}^3}{113.04 \, \text{cm}^3}
\]
### Step 6: Compute the number of spherical lead shots
Calculating the above expression:
\[
\text{Number of shots} \approx \frac{6336}{113.04} \approx 56
\]
### Final Answer
Thus, the number of spherical lead shots that can be made from the solid cuboid of lead is approximately **56**.
---
