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: Convert every measurement to a single unit (centimetres) to avoid decimal errors. Brick: \( 25 \times 11.25 \times 6 \) cm. Wall: \( 800 \times 600 \times 22.5 \) cm (since \( 8 \text{ m} = 800 \text{ cm} \) and \( 6 \text{ m} = 600 \text{ cm} \)).

Step 2: Write the number of bricks as a ratio of volumes: \[ n = \frac{800 \times 600 \times 22.5}{25 \times 11.25 \times 6} \]

Step 3: Cancel common factors before multiplying out: \( \frac{800}{25} = 32 \), \( \frac{22.5}{11.25} = 2 \), and \( \frac{600}{6} = 100 \), leaving \[ n = 32 \times 2 \times 100 \]

Step 4: Multiply the simplified factors: \[ n = 32 \times 2 \times 100 = 6400 \] \[ \boxed{6400 \text{ bricks}} \]