Find the number of bricks each of dimensions 25 cm x 12.5 cm x 7.5 cm to make a wall of dimensions 5 m x 3 m x 20 m.

Options

A. 120000
B. 135000
C. 128000
D. 140000

Answer

To find the number of bricks needed to construct a wall, we will follow these steps:

### Step 1: Convert the dimensions of the wall to centimeters.
The dimensions of the wall are given in meters. We need to convert these measurements to centimeters since the dimensions of the bricks are in centimeters.

- Wall dimensions:
- Length = 5 m = 5 × 100 = 500 cm
- Height = 3 m = 3 × 100 = 300 cm
- Width = 20 m = 20 × 100 = 2000 cm

### Step 2: Calculate the volume of the wall.
The volume of a rectangular prism (like our wall) is calculated using the formula:
\[ \text{Volume} = \text{Length} \times \text{Height} \times \text{Width} \]

Substituting in the dimensions we converted:
\[ \text{Volume of the wall} = 500 \, \text{cm} \times 300 \, \text{cm} \times 2000 \, \text{cm} \]

Calculating this gives:
\[ \text{Volume of the wall} = 500 \times 300 \times 2000 = 300,000,000 \, \text{cm}^3 \]

### Step 3: Calculate the volume of one brick.
The dimensions of one brick are given as:
- Length = 25 cm
- Width = 12.5 cm
- Height = 7.5 cm

Using the volume formula:
\[ \text{Volume of one brick} = 25 \, \text{cm} \times 12.5 \, \text{cm} \times 7.5 \, \text{cm} \]

Calculating this gives:
\[ \text{Volume of one brick} = 25 \times 12.5 \times 7.5 = 2343.75 \, \text{cm}^3 \]

### 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:
\[ \text{Number of bricks} = \frac{\text{Volume of the wall}}{\text{Volume of one brick}} \]

Substituting in the volumes we calculated:
\[ \text{Number of bricks} = \frac{300,000,000 \, \text{cm}^3}{2343.75 \, \text{cm}^3} \]

Calculating this gives:
\[ \text{Number of bricks} \approx 12800 \]

### Final Answer:
The number of bricks required to make the wall is **12800**.

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