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

Options

A. 11000
B. 11100
C. 11200
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 the wall can be calculated using the formula for the volume of a cuboid:
\[ V = \text{length} \times \text{width} \times \text{height} \]
Given dimensions of the wall are:
- Length = 270 cm
- Width = 300 cm
- Height = 350 cm

Substituting the values:
\[ V = 270 \, \text{cm} \times 300 \, \text{cm} \times 350 \, \text{cm} \]

### Step 2: Calculate the total volume of the wall
Calculating the volume:
\[ V = 270 \times 300 \times 350 = 28350000 \, \text{cm}^3 \]

### Step 3: Adjust for the volume occupied by mortar
Since \( \frac{1}{8} \) of the wall's volume is occupied by mortar, we need to calculate the volume that is actually occupied by bricks:
\[ \text{Volume occupied by bricks} = V \times \left(1 - \frac{1}{8}\right) = V \times \frac{7}{8} \]
Calculating this:
\[ \text{Volume occupied by bricks} = 28350000 \times \frac{7}{8} = 24806250 \, \text{cm}^3 \]

### Step 4: Calculate the volume of one brick
The dimensions of one brick are:
- Length = 22.5 cm
- Width = 11.25 cm
- Height = 8.75 cm

Calculating the volume of one brick:
\[ \text{Volume of one brick} = 22.5 \, \text{cm} \times 11.25 \, \text{cm} \times 8.75 \, \text{cm} \]
Calculating this:
\[ \text{Volume of one brick} = 22.5 \times 11.25 \times 8.75 = 2203.125 \, \text{cm}^3 \]

### Step 5: Calculate the number of bricks used
To find the number of bricks used, we divide the total volume occupied by bricks by the volume of one brick:
\[ \text{Number of bricks} = \frac{\text{Volume occupied by bricks}}{\text{Volume of one brick}} = \frac{24806250}{2203.125} \]
Calculating this:
\[ \text{Number of bricks} \approx 11250 \]

### Final Answer
The number of bricks used to construct the wall is approximately **11250**.

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