How many bricks each measuring is `25 cmxx11.5 cm xx6` cm will be needed to construct a wall 8 m long, 6 m high and 23 cm thick?

Options

A. A)3200
B. B)4800
C. C)6400
D. D)7200

Answer

To find out how many bricks are needed to construct a wall, we can follow these steps:

### Step 1: Calculate the volume of one brick.
The dimensions of one brick are given as:
- Length = 25 cm
- Width = 11.5 cm
- Height = 6 cm

The volume \( V \) of one brick can be calculated using the formula for the volume of a rectangular prism:
\[ V = \text{Length} \times \text{Width} \times \text{Height} \]
Substituting the values:
\[ V = 25 \, \text{cm} \times 11.5 \, \text{cm} \times 6 \, \text{cm} \]
Calculating this gives:
\[ V = 1725 \, \text{cm}^3 \]

### Step 2: Calculate the volume of the wall.
The dimensions of the wall are given as:
- Length = 8 m
- Height = 6 m
- Thickness = 23 cm

First, we need to convert the length and height from meters to centimeters:
- Length = \( 8 \, \text{m} = 8 \times 100 = 800 \, \text{cm} \)
- Height = \( 6 \, \text{m} = 6 \times 100 = 600 \, \text{cm} \)

Now, we can calculate the volume \( V_w \) of the wall:
\[ V_w = \text{Length} \times \text{Height} \times \text{Thickness} \]
Substituting the values:
\[ V_w = 800 \, \text{cm} \times 600 \, \text{cm} \times 23 \, \text{cm} \]
Calculating this gives:
\[ V_w = 11088000 \, \text{cm}^3 \]

### Step 3: Calculate the number of bricks required.
To find the number of bricks \( N \), we divide the total volume of the wall by the volume of one brick:
\[ N = \frac{V_w}{V} \]
Substituting the values:
\[ N = \frac{11088000 \, \text{cm}^3}{1725 \, \text{cm}^3} \]
Calculating this gives:
\[ N \approx 6415.65 \]
Since we cannot have a fraction of a brick, we round this down to the nearest whole number:
\[ N = 6415 \]

### Final Answer:
The number of bricks needed to construct the wall is **6415 bricks**.

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