Question

How many bricks each measuring 25cm \(\times\) 11.25cm \(\times\) 6cm will be needed to build a wall of size 8m \(\times\) 6m \(\times\) 22.5cm?

• A. 5600
• B. 600
• C. 6400
• D. 7200

Hint:

Always convert all dimensions to a consistent unit (either all cm or all m) *before* calculating volumes. This prevents errors and simplifies calculations. For example, $22.5 \text{ cm} = 0.225 \text{ m}$.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
The problem asks for the number of bricks required to build a wall of given dimensions. This involves calculating volumes and ensuring consistent units.

Step 2: Key Formula or Approach:
1. Calculate the volume of one brick.
2. Calculate the volume of the wall.
3. Ensure all dimensions are in the same unit (e.g., meters or centimeters).
4. Number of bricks = $\frac{\text{Volume of wall}}{\text{Volume of one brick}}$.

Step 3: Detailed Explanation:
Dimensions of one brick:
Length = 25 cm = 0.25 m
Width = 11.25 cm = 0.1125 m
Height = 6 cm = 0.06 m
Volume of one brick = $0.25 \times 0.1125 \times 0.06 \text{ m}^3 = 0.0016875 \text{ m}^3$.
Dimensions of the wall:
Length = 8 m
Width = 6 m
Height = 22.5 cm = 0.225 m
Volume of the wall = $8 \times 6 \times 0.225 \text{ m}^3 = 48 \times 0.225 \text{ m}^3 = 10.8 \text{ m}^3$.
Number of bricks needed:
Number of bricks = $\frac{\text{Volume of wall}}{\text{Volume of one brick}} = \frac{10.8 \text{ m}^3}{0.0016875 \text{ m}^3}$.
To simplify the division:
Number of bricks = $\frac{10.8}{0.0016875} = \frac{10800000}{16875} = 6400$.

Step 4: Final Answer:
6400 bricks will be needed.

Answer 2

Instead of computing volumes directly, we can work out how many bricks fit along each dimension of the wall separately and multiply those counts together, a purely dimensional-fit approach that reaches the same total.

1. 5600: Laying the bricks with their 25 cm length along the 8 m length of the wall gives \( \frac{800}{25} = 32 \) bricks per row. Along the 6 m height, stacking bricks using their 6 cm dimension gives \( \frac{600}{6} = 100 \) layers. Since the wall's 22.5 cm thickness exactly fits two bricks laid width-wise (\( 11.25 \times 2 = 22.5 \)), each layer needs 2 bricks across the thickness. Multiplying \( 32 \times 100 \times 2 = 6400 \), not 5600, so this option is too low.
2. 600: This figure is far too small to fill a wall of this scale; it does not correspond to any consistent combination of the three dimensional counts worked out above (32, 100, and 2), so it can be ruled out immediately.
3. 6400: Combining the three dimensional counts, 32 bricks along the length, 100 layers up the height, and 2 bricks across the thickness, gives \( 32 \times 100 \times 2 = 6400 \) bricks in total, which matches this option exactly.
4. 7200: This value overshoots the dimensional-fit count; there is no way to arrange the given brick dimensions inside the given wall dimensions to reach this many bricks without leaving gaps or overlaps, so it is too high.

Fitting the bricks along each of the wall's three dimensions and multiplying the counts together confirms the total number needed.

Therefore, the correct answer is 6400.