A mason constructs a wall of dimensions 270 cm $\times$ 300 cm $\times$ 350 cm with the bricks each of size 22.5 cm $\times$ 11.25 cm $\times$ 8.75 cm and it is assumed that $\frac{1}{8}$ space is covered by the mortar. Then the number of bricks used to construct the wall is ______.

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A mason constructs a wall of dimensions 270 cm $\times$ 300 cm $\times$ 350 cm with the bricks each of size 22.5 cm $\times$ 11.25 cm $\times$ 8.75 cm and it is assumed that $\frac{1}{8}$ space is covered by the mortar. Then the number of bricks used to construct the wall is 11200. Explanation: Volume of the wall = 270 $\times$ 300 $\times$ 350 ...[∵ Volume of cuboid = length $\times$ breadth $\times$ height] = 28350000 cm3 Since, $\frac{1}{8}$ space of wall is covered by mortar. So, remaining space of wall = Volume of wall – Volume of mortar = 28350000 - 28350000 xx $\frac{1}{8}$ = 28350000 – 3543750 = 24806250 cm3 Now, volume of one brick = 22.5 $\times$ 11.25 $\times$ 8.75 ...[∵ Volume of cuboid = length $\times$ breadth $\times$ height] = 2214.844 cm3 $\therefore$ Required number of bricks = $\frac{24806250}{2214}$.844 = 11200 (approx) Hence, the number of bricks used to construct the wall is 11200.

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