Each brick measures 25 cm by 11.25 cm by 6 cm. A wall has dimensions 8 m by 6 m by 22.5 cm (that is, thickness 22.5 cm). Assuming that there is no space for mortar, how many such bricks will be needed to build the wall completely?

Introduction / Context:
This is a typical volume based problem involving bricks and walls. The question gives the dimensions of a single brick and the dimensions of a wall and asks how many bricks are required to construct the wall. The assumption is that there is no space for mortar and that the wall is solid. The key skill tested is unit conversion between metres and centimetres and division of volumes to count identical bricks.

Given Data / Assumptions:

• Brick dimensions: 25 cm by 11.25 cm by 6 cm.
• Wall dimensions: 8 m by 6 m by 22.5 cm.
• Since 1 m = 100 cm, wall length = 800 cm, wall height = 600 cm, wall thickness = 22.5 cm.
• Wall is solid and there is no volume for mortar.
• All bricks are placed without gaps.

Concept / Approach:
The number of bricks required is given by:
Number of bricks = Volume of wall / Volume of one brick We must ensure that all dimensions are in the same units before computing volumes. Since brick dimensions are in centimetres, we convert the wall dimensions to centimetres as well.

Step-by-Step Solution:
Step 1: Convert wall dimensions to centimetres. Wall length L = 8 m = 800 cm. Wall height H = 6 m = 600 cm. Wall thickness T = 22.5 cm. Step 2: Compute volume of the wall. Volume wall = L * H * T Volume wall = 800 * 600 * 22.5 cubic centimetres. Volume wall = 10,800,000 cubic centimetres. Step 3: Compute volume of one brick. Volume brick = 25 * 11.25 * 6 cubic centimetres. Volume brick = 1687.5 cubic centimetres. Step 4: Compute number of bricks. Number of bricks = 10,800,000 / 1687.5 Number of bricks = 6400. Thus, 6400 bricks are required to build the wall.

Verification / Alternative check:
We can simplify the division by factoring: 1687.5 = 16875 / 10. Then 10,800,000 / 1687.5 = (10,800,000 * 10) / 16875. Both numerator and denominator are divisible by 375, giving 288,000 / 750, which simplifies to 6400. This algebraic simplification confirms the numerical result.

Why Other Options Are Wrong:
Option A (5600) and Option D (7200) represent miscalculations usually caused by rounding the thickness or brick measurements improperly. Option B (600) and Option E (4800) are far too small and would correspond to an unrealistic wall volume relative to brick size. Only 6400 matches the precise volume ratio.

Common Pitfalls:
The main source of error is forgetting to convert metres to centimetres, leading to inconsistent units. Another frequent mistake is rounding 11.25 or 22.5 too early, which slightly changes the computed number of bricks. Always maintain exact decimals until the final division and ensure all three wall dimensions are included when computing volume.

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