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.