To solve the problem of how many bricks are required to construct a wall, we will follow these steps:
### Step 1: Calculate the volume of the wall.
The wall is in the shape of a cuboid, and its volume can be calculated using the formula:
\[ \text{Volume} = \text{Length} \times \text{Height} \times \text{Thickness} \]
Given:
- Length of the wall = 24 m
- Height of the wall = 5 m
- Thickness of the wall = 0.25 m
First, we convert the dimensions from meters to centimeters (since the dimensions of the bricks are given in centimeters):
- Length = 24 m = 2400 cm
- Height = 5 m = 500 cm
- Thickness = 0.25 m = 25 cm
Now, we can calculate the volume:
\[
\text{Volume of the wall} = 2400 \, \text{cm} \times 500 \, \text{cm} \times 25 \, \text{cm}
\]
\[
= 2400 \times 500 = 1200000 \, \text{cm}^2
\]
\[
= 1200000 \times 25 = 30000000 \, \text{cm}^3
\]
### Step 2: Calculate the volume occupied by cement and sand mixture.
We are told that 5% of the wall is occupied by a cement and sand mixture.
To find the volume occupied by this mixture:
\[
\text{Volume occupied by cement and sand} = 5\% \text{ of Volume of the wall}
\]
\[
= \frac{5}{100} \times 30000000 \, \text{cm}^3 = 1500000 \, \text{cm}^3
\]
### Step 3: Calculate the effective volume occupied by bricks.
To find the volume that will be occupied by the bricks, we subtract the volume occupied by the cement and sand from the total volume of the wall:
\[
\text{Volume occupied by bricks} = \text{Volume of the wall} - \text{Volume occupied by cement and sand}
\]
\[
= 30000000 \, \text{cm}^3 - 1500000 \, \text{cm}^3 = 28500000 \, \text{cm}^3
\]
### Step 4: Calculate the volume of one brick.
The volume of one brick can be calculated using the formula:
\[
\text{Volume of one brick} = \text{Length} \times \text{Width} \times \text{Height}
\]
Given:
- Length of the brick = 25 cm
- Width of the brick = 12.5 cm
- Height of the brick = 7.5 cm
Calculating the volume:
\[
\text{Volume of one brick} = 25 \, \text{cm} \times 12.5 \, \text{cm} \times 7.5 \, \text{cm}
\]
\[
= 25 \times 12.5 = 312.5 \, \text{cm}^2
\]
\[
= 312.5 \times 7.5 = 2343.75 \, \text{cm}^3
\]
### Step 5: Calculate the number of bricks required.
Finally, we can find the number of bricks required by dividing the effective volume occupied by bricks by the volume of one brick:
\[
\text{Number of bricks} = \frac{\text{Volume occupied by bricks}}{\text{Volume of one brick}}
\]
\[
= \frac{28500000 \, \text{cm}^3}{2343.75 \, \text{cm}^3} \approx 12160
\]
### Final Answer:
The number of bricks required is approximately **12160**.
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