How many bricks will be required to construct a wall 3 m long, 1.5 m high and 0.4 m thick, if each brick measures 30 cm x 15 cm x 8 cm ?

Options

A. 502
B. 550
C. 500
D. 501

Answer

To find out how many bricks are required to construct a wall with given dimensions, we will follow these steps:

### Step 1: Convert the dimensions of the wall from meters to centimeters.
The dimensions of the wall are given as:
- Length = 3 m
- Height = 1.5 m
- Thickness = 0.4 m

To convert these measurements to centimeters:
- 1 m = 100 cm
- Length = 3 m × 100 cm/m = 300 cm
- Height = 1.5 m × 100 cm/m = 150 cm
- Thickness = 0.4 m × 100 cm/m = 40 cm

### Step 2: Calculate the volume of the wall.
The volume \( V \) of the wall can be calculated using the formula:
\[ V = \text{Length} \times \text{Height} \times \text{Thickness} \]

Substituting the values:
\[ V = 300 \, \text{cm} \times 150 \, \text{cm} \times 40 \, \text{cm} \]
\[ V = 300 \times 150 \times 40 \]
\[ V = 1,800,000 \, \text{cm}^3 \]

### Step 3: Calculate the volume of a single brick.
The dimensions of each brick are given as:
- Length = 30 cm
- Width = 15 cm
- Height = 8 cm

The volume \( V_b \) of a single brick is calculated as:
\[ V_b = \text{Length} \times \text{Width} \times \text{Height} \]

Substituting the values:
\[ V_b = 30 \, \text{cm} \times 15 \, \text{cm} \times 8 \, \text{cm} \]
\[ V_b = 30 \times 15 \times 8 \]
\[ V_b = 3600 \, \text{cm}^3 \]

### Step 4: Calculate the number of bricks required.
To find the number of bricks needed, 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 the values:
\[ \text{Number of bricks} = \frac{1,800,000 \, \text{cm}^3}{3600 \, \text{cm}^3} \]
\[ \text{Number of bricks} = 500 \]

### Final Answer:
Therefore, the number of bricks required to construct the wall is **500**.

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