How many bricks, each measuring `25 cm xx 1.25 cm xx 6 cm`, will be needed to build a wall 8 m long, 6m high and 22.5 cm thick?

Options

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

Answer

To solve the problem of how many bricks are needed to build a wall with the given dimensions, we will follow these steps:

### Step 1: Convert all measurements to the same unit
The dimensions of the wall are given in meters and centimeters. To make calculations easier, we will convert everything 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 a rectangular prism (which is the shape of the wall) is given by the formula:
\[ \text{Volume} = \text{Length} \times \text{Height} \times \text{Thickness} \]

Substituting the values we have:
\[ \text{Volume of the wall} = 800 \, \text{cm} \times 600 \, \text{cm} \times 22.5 \, \text{cm} \]

### Step 3: Calculate the volume of one brick
The dimensions of one brick are given as:
- Length = 25 cm
- Width = 1.25 cm
- Height = 6 cm

Using the same volume formula:
\[ \text{Volume of one brick} = 25 \, \text{cm} \times 1.25 \, \text{cm} \times 6 \, \text{cm} \]

### Step 4: Calculate the number of bricks needed
To find the number of bricks required, 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:
\[ \text{Volume of the wall} = 800 \times 600 \times 22.5 = 10800000 \, \text{cm}^3 \]

2. Calculate the volume of one brick:
\[ \text{Volume of one brick} = 25 \times 1.25 \times 6 = 187.5 \, \text{cm}^3 \]

3. Calculate the number of bricks:
\[ \text{Number of bricks} = \frac{10800000}{187.5} \approx 57600 \]

### Final Answer
The number of bricks needed to build the wall is approximately **57,600 bricks**.

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