A mason constructs a wall of dimension `270` `cm` `xx` `300` `cm` `xx` `350` `cm` with the bricks each of size `22.5` `cm` `xx` `11.25` `cm` `xx` `8.75` `cm` and it is assumed that `(1)/(8)` space is covered by the mortar. Then, the number of bricks used to construct the wall is

Options

A. `11100`
B. `11200`
C. `11000`
D. `11300`

Explanation

To find the number of bricks used to construct 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:
\[ V = \text{Length} \times \text{Breadth} \times \text{Height} \]
For the wall, the dimensions are:
- Length = 270 cm
- Breadth = 300 cm
- Height = 350 cm

Calculating the volume:
\[ V_{\text{wall}} = 270 \, \text{cm} \times 300 \, \text{cm} \times 350 \, \text{cm} \]
\[ V_{\text{wall}} = 28350000 \, \text{cm}^3 \]

### Step 2: Adjust for Mortar
Since \( \frac{1}{8} \) of the volume is covered by mortar, the volume occupied by bricks is:
\[ V_{\text{bricks}} = V_{\text{wall}} \times \frac{7}{8} \]
Calculating the volume occupied by bricks:
\[ V_{\text{bricks}} = 28350000 \times \frac{7}{8} = 24806250 \, \text{cm}^3 \]

### Step 3: Calculate the Volume of One Brick
The dimensions of one brick are:
- Length = 22.5 cm
- Breadth = 11.25 cm
- Height = 8.75 cm

Using the volume formula for the brick:
\[ V_{\text{brick}} = 22.5 \, \text{cm} \times 11.25 \, \text{cm} \times 8.75 \, \text{cm} \]
Calculating the volume of one brick:
\[ V_{\text{brick}} = 22.5 \times 11.25 \times 8.75 = 2214.84375 \, \text{cm}^3 \]

### Step 4: Calculate the Number of Bricks
To find the number of bricks used, divide the volume occupied by bricks by the volume of one brick:
\[ N = \frac{V_{\text{bricks}}}{V_{\text{brick}}} \]
Calculating the number of bricks:
\[ N = \frac{24806250}{2214.84375} \approx 11200 \]

### Final Answer
The number of bricks used to construct the wall is approximately **11200**.

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