How many bricks will be required to construct a wall 8m long, 6m high and 22.5 cm thick if each brick measures `(25 cm xx 11.25 cm xx 6 cm)` ?

Options

A. 4800
B. 5600
C. 6400
D. 5200

Answer

To determine how many bricks are required to construct a wall that is 8 meters long, 6 meters high, and 22.5 cm thick, we will follow these steps:

### Step 1: Convert all measurements to the same unit
Since the dimensions of the wall are given in meters and the dimensions of the brick are in centimeters, we will convert the wall's dimensions from meters 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:

\[ \text{Volume of the wall} = 800 \, \text{cm} \times 600 \, \text{cm} \times 22.5 \, \text{cm} \]

Calculating this gives:

\[ \text{Volume of the wall} = 800 \times 600 \times 22.5 = 10800000 \, \text{cm}^3 \]

### Step 3: Calculate the volume of one brick
The volume of one brick can also be calculated using the formula for the volume of a rectangular prism:

\[ \text{Volume of one brick} = \text{Length} \times \text{Width} \times \text{Height} \]

Substituting the dimensions of the brick:

\[ \text{Volume of one brick} = 25 \, \text{cm} \times 11.25 \, \text{cm} \times 6 \, \text{cm} \]

Calculating this gives:

\[ \text{Volume of one brick} = 25 \times 11.25 \times 6 = 1687.5 \, \text{cm}^3 \]

### 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:

\[ \text{Number of bricks} = \frac{\text{Volume of the wall}}{\text{Volume of one brick}} = \frac{10800000 \, \text{cm}^3}{1687.5 \, \text{cm}^3} \]

Calculating this gives:

\[ \text{Number of bricks} = \frac{10800000}{1687.5} \approx 6400 \]

### Final Answer
The number of bricks required to construct the wall is approximately **6400 bricks**.

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