A wall 24 m long, 0.4 m thick and 6 m high is constructed with bricks each of dimensions 25 cm \(\times\) 16 cm \(\times\) 10 cm. If the mortar occupies \(\dfrac{1}{10}\) of the volume of the wall, find the number of bricks used.
12,960 bricks
Step 1: Find the volume of the wall.
The formula for volume is: length × thickness × height.
Wall volume = \(24 \times 0.4 \times 6 = 57.6\,\text{m}^3\).
Step 2: Account for mortar.
We are told that mortar occupies \(\dfrac{1}{10}\) of the total wall volume.
So, volume actually filled with bricks = \(\dfrac{9}{10} \times 57.6 = 51.84\,\text{m}^3\).
Step 3: Convert brick dimensions to metres (SI unit).
1 cm = 0.01 m.
Brick length = \(25\,\text{cm} = 0.25\,\text{m}\).
Brick width = \(16\,\text{cm} = 0.16\,\text{m}\).
Brick height = \(10\,\text{cm} = 0.10\,\text{m}\).
Step 4: Find the volume of one brick.
Brick volume = \(0.25 \times 0.16 \times 0.10 = 0.004\,\text{m}^3\).
Step 5: Find number of bricks.
Number of bricks = \(\dfrac{\text{Volume of bricks in wall}}{\text{Volume of one brick}}\).
\(= \dfrac{51.84}{0.004} = 12960\).
Final Answer: 12,960 bricks are needed.