How many bricks, each measuring 25 cm `xx` 11.25 cm `xx` 6 cm will be needed to build a wall 8 m long, 6 m high and 22.5 cm thick?

Options

A. 5600
B. 6000
C. 6400
D. 7200

Answer

To find out how many bricks are needed to build the wall, we will follow these steps:

### Step 1: Convert the dimensions of the wall to centimeters.
The wall dimensions are given in meters, so we need to convert them to centimeters:
- Length of the wall = 8 m = 8 × 100 cm = 800 cm
- Height of the wall = 6 m = 6 × 100 cm = 600 cm
- Thickness of the wall = 22.5 cm (already in cm)

### Step 2: Calculate the volume of the wall.
The volume of the wall can be calculated using the formula for the volume of a rectangular prism:
\[ \text{Volume of the wall} = \text{Length} \times \text{Height} \times \text{Thickness} \]
Substituting the values:
\[ \text{Volume of the wall} = 800 \, \text{cm} \times 600 \, \text{cm} \times 22.5 \, \text{cm} \]

### Step 3: Calculate the volume of one brick.
The dimensions of one brick are given as 25 cm × 11.25 cm × 6 cm. We can calculate the volume of one brick using the same formula:
\[ \text{Volume of one brick} = \text{Length} \times \text{Width} \times \text{Height} \]
Substituting the values:
\[ \text{Volume of one brick} = 25 \, \text{cm} \times 11.25 \, \text{cm} \times 6 \, \text{cm} \]

### Step 4: Calculate the number of bricks required.
To find the number of bricks needed, we divide the volume of the wall by the volume of one brick:
\[ \text{Number of bricks} = \frac{\text{Volume of the wall}}{\text{Volume of one brick}} \]

### Step 5: Perform the calculations.
1. Calculate the volume of the wall:
\[ \text{Volume of the wall} = 800 \times 600 \times 22.5 = 10,800,000 \, \text{cm}^3 \]

2. Calculate the volume of one brick:
\[ \text{Volume of one brick} = 25 \times 11.25 \times 6 = 1,687.5 \, \text{cm}^3 \]

3. Calculate the number of bricks:
\[ \text{Number of bricks} = \frac{10,800,000}{1,687.5} \approx 6400 \]

### Final Answer:
You will need approximately **6400 bricks** to build the wall.

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