A wall 15 m long, 30 cm wide and 4m high is made of bricks, each measuring `(22cm xx 12.5 cm xx 7.5 cm)`. If `(1)/(12)` of the total volume of the wall consits of mortar, how many bricks are there in the wall ?

Explanation

To find the number of bricks in the wall, we will follow these steps:

### Step 1: Calculate the Volume of the Wall
The volume \( V \) of a cuboid is given by the formula:
\[ V = \text{length} \times \text{breadth} \times \text{height} \]
Given:
- Length = 15 m
- Breadth = 30 cm = 0.30 m (since 1 m = 100 cm)
- Height = 4 m

Now, substituting the values:
\[ V = 15 \, \text{m} \times 0.30 \, \text{m} \times 4 \, \text{m} \]
\[ V = 15 \times 0.30 \times 4 = 18 \, \text{m}^3 \]

### Step 2: Calculate the Volume of Mortar
According to the problem, \(\frac{1}{12}\) of the total volume of the wall consists of mortar.
\[ \text{Volume of Mortar} = \frac{1}{12} \times \text{Volume of Wall} \]
Substituting the volume of the wall:
\[ \text{Volume of Mortar} = \frac{1}{12} \times 18 \, \text{m}^3 = 1.5 \, \text{m}^3 \]

### Step 3: Calculate the Volume of Bricks
The volume occupied by bricks is the total volume of the wall minus the volume of mortar:
\[ \text{Volume of Bricks} = \text{Volume of Wall} - \text{Volume of Mortar} \]
\[ \text{Volume of Bricks} = 18 \, \text{m}^3 - 1.5 \, \text{m}^3 = 16.5 \, \text{m}^3 \]

### Step 4: Calculate the Volume of One Brick
The volume \( V_b \) of one brick is given by:
\[ V_b = \text{length} \times \text{breadth} \times \text{height} \]
Given the dimensions of the brick:
- Length = 22 cm = 0.22 m
- Breadth = 12.5 cm = 0.125 m
- Height = 7.5 cm = 0.075 m

Now substituting the values:
\[ V_b = 0.22 \, \text{m} \times 0.125 \, \text{m} \times 0.075 \, \text{m} \]
\[ V_b = 0.22 \times 0.125 \times 0.075 = 0.00020625 \, \text{m}^3 \]

### Step 5: Calculate the Number of Bricks
To find the number of bricks, we divide the total volume of bricks by the volume of one brick:
\[ \text{Number of Bricks} = \frac{\text{Volume of Bricks}}{\text{Volume of One Brick}} \]
\[ \text{Number of Bricks} = \frac{16.5 \, \text{m}^3}{0.00020625 \, \text{m}^3} \]
Calculating this gives:
\[ \text{Number of Bricks} \approx 79999.999 \approx 80000 \]

### Final Answer
Thus, the number of bricks in the wall is approximately **80000**.

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