The total number of spherical bullets, each of diameter 5 decimeter, that can be made by utilizing the maximum of rectangular block of lead with 11 metre length, 10 metre breadth and 5 metre width is (assume that `pi gt 3`)

Options

A. A)equal to 8800
B. B)less than 800
C. C)equal to 8400
D. D)greater than 9000

Answer

To solve the problem of finding the total number of spherical bullets that can be made from a rectangular block of lead, we will follow these steps:

### Step 1: Calculate the volume of the rectangular block of lead.
The dimensions of the rectangular block are given as:
- Length = 11 meters
- Breadth = 10 meters
- Height = 5 meters

To find the volume \( V \) of the rectangular block, we use the formula:
\[ V = \text{Length} \times \text{Breadth} \times \text{Height} \]
Substituting the values:
\[ V = 11 \, \text{m} \times 10 \, \text{m} \times 5 \, \text{m} = 550 \, \text{m}^3 \]

### Step 2: Convert the volume from cubic meters to cubic decimeters.
Since 1 cubic meter is equal to 1000 cubic decimeters, we convert the volume:
\[ V = 550 \, \text{m}^3 \times 1000 \, \text{dm}^3/\text{m}^3 = 550000 \, \text{dm}^3 \]

### Step 3: Calculate the volume of one spherical bullet.
The diameter of each bullet is given as 5 decimeters, so the radius \( r \) is:
\[ r = \frac{\text{Diameter}}{2} = \frac{5 \, \text{dm}}{2} = 2.5 \, \text{dm} \]

The volume \( V_b \) of one spherical bullet is given by the formula:
\[ V_b = \frac{4}{3} \pi r^3 \]
Substituting the radius:
\[ V_b = \frac{4}{3} \pi (2.5 \, \text{dm})^3 \]
Calculating \( (2.5)^3 \):
\[ (2.5)^3 = 15.625 \, \text{dm}^3 \]
Now substituting back:
\[ V_b = \frac{4}{3} \pi \times 15.625 \]
Using \( \pi \approx 3 \):
\[ V_b \approx \frac{4}{3} \times 3 \times 15.625 = 4 \times 15.625 = 62.5 \, \text{dm}^3 \]

### Step 4: Calculate the total number of spherical bullets.
To find the total number of bullets \( n \), we divide the total volume of the rectangular block by the volume of one bullet:
\[ n = \frac{\text{Total Volume of Block}}{\text{Volume of One Bullet}} = \frac{550000 \, \text{dm}^3}{62.5 \, \text{dm}^3} \]
Calculating \( n \):
\[ n = \frac{550000}{62.5} = 8800 \]

### Final Answer:
The total number of spherical bullets that can be made is **8800**.

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