A wall of dimensions 270 cm \(\times\) 300 cm \(\times\) 350 cm is built with bricks of size 22.5 cm \(\times\) 11.25 cm \(\times\) 8.75 cm. If \(\dfrac{1}{8}\) of the space is covered by mortar, the number of bricks used is
11100
11200
11000
11300
Step 1: Find the volume of one brick.
Each brick has dimensions: \(22.5\,\text{cm} \times 11.25\,\text{cm} \times 8.75\,\text{cm}\).
So, volume of one brick = \(22.5 \times 11.25 \times 8.75 = 2214.84375\,\text{cm}^3\).
Step 2: Find the total volume of the wall (without considering mortar).
Wall dimensions = \(270\,\text{cm} \times 300\,\text{cm} \times 350\,\text{cm}\).
Total wall volume = \(270 \times 300 \times 350 = 28,350,000\,\text{cm}^3\).
Step 3: Adjust for mortar.
We are told \(\tfrac{1}{8}\) of the volume is filled with mortar, not bricks.
So, fraction available for bricks = \(1 - \tfrac{1}{8} = \tfrac{7}{8}\).
Usable volume = \(\tfrac{7}{8} \times 28,350,000 = 24,806,250\,\text{cm}^3\).
Step 4: Find how many bricks can fit in this usable volume.
Number of bricks = \(\dfrac{24,806,250}{2214.84375} \approx 11200\).
Final Answer: The number of bricks used is 11200.