How many bricks, each measuring 25 cm × 11.25 cm × 6 cm, are required to build a solid wall of dimensions 8 m × 6 m × 22.5 cm, assuming the wall is completely solid without gaps?

Introduction / Context:
This question is a classic volume-and-counting problem related to construction. We are given the dimensions of a wall and an individual brick, and we must determine how many such bricks are required to build the wall if it is completely solid. The problem checks understanding of unit conversion between metres and centimetres, volume calculation for cuboids, and the idea that the number of bricks equals total wall volume divided by volume of one brick.

Given Data / Assumptions:

• Dimensions of the wall: 8 m by 6 m by 22.5 cm.
• Dimensions of each brick: 25 cm by 11.25 cm by 6 cm.
• The wall is solid, with no gaps or mortar considered.
• Bricks are placed without cutting and fill the wall volume exactly.

Concept / Approach:
Both the wall and each brick are rectangular solids (cuboids). The number of bricks needed is:
Number of bricks = Volume of wall / Volume of one brick We must ensure all dimensions are in the same unit, preferably centimetres. So we convert the metre dimensions of the wall to centimetres before calculating volumes.

Step-by-Step Solution:
Convert wall dimensions: 8 m = 800 cm, 6 m = 600 cm, thickness = 22.5 cm. Volume of wall = 800 cm * 600 cm * 22.5 cm. Volume of wall = 800 * 600 * 22.5 = 10,800,000 cubic centimetres. Volume of one brick = 25 cm * 11.25 cm * 6 cm. Volume of one brick = 25 * 11.25 * 6 = 1687.5 cubic centimetres. Number of bricks = 10,800,000 / 1687.5. Compute: 10,800,000 / 1687.5 = 6400.

Verification / Alternative check:
We can simplify the fraction by factoring. Note that 1687.5 * 100 = 168750, and 10,800,000 * 100 = 1,080,000,000, so the ratio remains the same. Performing long division or using proportional reasoning confirms 6400 exactly. This matches one of the given options, which supports our calculation.

Why Other Options Are Wrong:
5600, 6000, 6800 and 7200 would imply either underestimating or overestimating the wall volume or miscalculating the brick volume. They usually arise from mistakes such as using 22 cm instead of 22.5 cm, or rounding 11.25 cm incorrectly. Only 6400 gives an exact integer count consistent with the precise geometric volumes.

Common Pitfalls:
A frequent error is mixing metres and centimetres in a single calculation, which gives incorrect volumes. Some students also round off 11.25 cm to 11 or 12, leading to wrong brick volumes. Others mis-handle the decimal thickness 22.5 cm or treat it as 22 cm. Always convert units carefully and handle decimals correctly before dividing to find the number of bricks.

Final Answer:
The number of bricks required to build the wall is 6400.