**Question:**

A mason constructs a wall of dimensions $(270 \mathrm{~cm} \times 300 \mathrm{~cm} \times 350 \mathrm{~cm})$ with bricks, each of size $(22.5 \mathrm{~cm} \times 11.25 \mathrm{~cm} \times 8.75 \mathrm{~cm})$ and it is assumed that $\frac{1}{8}$

space is covered by the mortar. Number of bricks used to construct the wall is

(a) 11000

(b) 11100

(c) 11200

(d) 11300

**Solution:**

(c) 11200

Volume of wall $=270 \times 300 \times 350 \mathrm{~cm}^{3}$

$\frac{1}{8}$ th of the wall is covered with mortar.

So,

Volume of the wall filled with bricks $=\left(\frac{7}{8} \times 270 \times 300 \times 350\right) \mathrm{cm}^{3}$

Volume of each brick $=\left(\frac{225}{10} \times \frac{1125}{100} \times \frac{875}{100}\right) \mathrm{cm}^{3}$

$=\left(\frac{9 \times 22 \times 32}{32}\right) \mathrm{cm}^{3}$

Number of bricks used to construct the wall $=\frac{\text { Volume of the wall composed of bricks }}{\text { Volulme of each brick }}$

$=\frac{7 \times 270 \times 300 \times 350 \times 32}{8 \times 9 \times 225 \times 35}$

$=11200$

Hence, the number of bricks used to construct the wall is 11200.