How many bricks will be required to construct a wall 13.5 m long, 6m high and 22.5 cm thick if each brick measures (27cm`xx12.5cmxx9cm`) ?

Options

A. 6000
B. 7500
C. 5000
D. 3750

Answer

To find the number of bricks required to construct the wall, we can follow these steps:

### Step 1: Convert the dimensions of the wall to centimeters.
- The length of the wall is given as 13.5 m.
- Convert to cm:
\[ 13.5 \, \text{m} = 13.5 \times 100 = 1350 \, \text{cm} \]
- The height of the wall is given as 6 m.
- Convert to cm:
\[ 6 \, \text{m} = 6 \times 100 = 600 \, \text{cm} \]
- The thickness of the wall is already given as 22.5 cm.

### Step 2: Calculate the volume of the wall.
- The volume \( V \) of the wall can be calculated using the formula:
\[ V = \text{length} \times \text{height} \times \text{thickness} \]
- Substituting the values:
\[ V = 1350 \, \text{cm} \times 600 \, \text{cm} \times 22.5 \, \text{cm} \]

### Step 3: Calculate the volume of one brick.
- The dimensions of one brick are given as:
- Length = 27 cm
- Breadth = 12.5 cm
- Height = 9 cm
- The volume \( V_b \) of one brick is:
\[ V_b = \text{length} \times \text{breadth} \times \text{height} \]
- Substituting the values:
\[ V_b = 27 \, \text{cm} \times 12.5 \, \text{cm} \times 9 \, \text{cm} \]

### Step 4: Set up the equation to find the number of bricks.
- Let \( n \) be the number of bricks required. The total volume of the bricks must equal the volume of the wall:
\[ n \times V_b = V \]
- Rearranging gives:
\[ n = \frac{V}{V_b} \]

### Step 5: Substitute the volumes into the equation.
- Substitute the calculated volumes:
\[ n = \frac{1350 \times 600 \times 22.5}{27 \times 12.5 \times 9} \]

### Step 6: Calculate the values.
- Calculate the volume of the wall:
\[ V = 1350 \times 600 \times 22.5 = 18225000 \, \text{cm}^3 \]
- Calculate the volume of one brick:
\[ V_b = 27 \times 12.5 \times 9 = 3037.5 \, \text{cm}^3 \]
- Now substitute these values into the equation for \( n \):
\[ n = \frac{18225000}{3037.5} \approx 6000 \]

### Final Answer:
- The number of bricks required to construct the wall is approximately **6000 bricks**.

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