Find the number of bricks required to construct a wall of dimensions `3 m xx 1.5 m xx 0.4 m`, if the dimension of a brick is `30 cm xx 15 cm xx 8 cm`.

Answer

To find the number of bricks required to construct a wall of dimensions 3 m x 1.5 m x 0.4 m using bricks of dimensions 30 cm x 15 cm x 8 cm, we will follow these steps:

### Step 1: Calculate the Volume of the Wall
The volume \( V \) of a cuboid (the wall) is given by the formula:
\[ V = \text{Length} \times \text{Breadth} \times \text{Height} \]
Substituting the dimensions of the wall:
\[ V = 3 \, \text{m} \times 1.5 \, \text{m} \times 0.4 \, \text{m} \]
Calculating this:
\[ V = 3 \times 1.5 = 4.5 \, \text{m}^2 \]
\[ V = 4.5 \times 0.4 = 1.8 \, \text{m}^3 \]

### Step 2: Calculate the Volume of One Brick
The volume \( V_b \) of a brick is also given by the formula for the volume of a cuboid:
\[ V_b = \text{Length} \times \text{Breadth} \times \text{Height} \]
Substituting the dimensions of the brick (converted to meters):
\[ V_b = 0.3 \, \text{m} \times 0.15 \, \text{m} \times 0.08 \, \text{m} \]
Calculating this:
\[ V_b = 0.3 \times 0.15 = 0.045 \, \text{m}^2 \]
\[ V_b = 0.045 \times 0.08 = 0.0036 \, \text{m}^3 \]

### Step 3: Convert the Volume of the Wall to Cubic Centimeters
Since the volume of the brick is in cubic meters, we need to convert the volume of the wall from cubic meters to cubic centimeters.
1 cubic meter = \( 1,000,000 \) cubic centimeters (or \( 10^6 \) cm³).
\[ V = 1.8 \, \text{m}^3 = 1.8 \times 10^6 \, \text{cm}^3 = 1,800,000 \, \text{cm}^3 \]

### Step 4: Calculate the Number of Bricks Required
To find the number of bricks required, we divide the volume of the wall by the volume of one brick:
\[ \text{Number of bricks} = \frac{V}{V_b} = \frac{1,800,000 \, \text{cm}^3}{3,600 \, \text{cm}^3} \]
Calculating this:
\[ \text{Number of bricks} = \frac{1,800,000}{3,600} = 500 \]

### Final Answer
The number of bricks required to construct the wall is **500 bricks**.

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