How many bricks each measuring 25 cm x 11.5 cm x 6 cm will be needed to construct a wall 8 m long, 6 m high and 23 cm thick ?

Question

Accepted Answer

To determine how many bricks are needed to construct the wall, we need to calculate the volume of the wall and the volume of a single brick, and then divide the wall's volume by the brick's volume.

1. **Calculate the volume of the wall:**
   - The dimensions of the wall are given as 8 meters long, 6 meters high, and 23 centimeters thick.
   - First, convert all dimensions to centimeters to match the brick's dimensions:
     - Length: 8 meters = 800 centimeters
     - Height: 6 meters = 600 centimeters
     - Thickness: 23 centimeters
   - Volume of the wall = Length × Height × Thickness
   - Volume of the wall = 800 cm × 600 cm × 23 cm = 11,040,000 cubic centimeters

2. **Calculate the volume of a single brick:**
   - The dimensions of a brick are given as 25 cm × 11.5 cm × 6 cm.
   - Volume of a brick = 25 cm × 11.5 cm × 6 cm = 1,725 cubic centimeters

3. **Calculate the number of bricks needed:**
   - Number of bricks = Volume of the wall / Volume of a brick
   - Number of bricks = 11,040,000 cm³ / 1,725 cm³ ≈ 6400

Therefore, the correct number of bricks needed is 6400, which corresponds to Option 3.

**Explanation of why other options are incorrect:**

- **Option 1 (3200):** This option is incorrect because it significantly underestimates the number of bricks needed. The calculation shows that 6400 bricks are required, which is double the amount suggested by this option.

- **Option 2 (4800):** This option is also incorrect as it underestimates the number of bricks. The calculated requirement is 6400 bricks, which is 1600 more than this option suggests.

- **Option 4 (7200):** This option overestimates the number of bricks needed. The calculation shows that only 6400 bricks are required, making this option 800 bricks too many.

In conclusion, the correct answer is Option 3, as it accurately reflects the number of bricks needed based on the given dimensions and calculations.