Question

A mason constructs a wall of dimensions (270 cm × 300 cm × 350 cm) with bricks, each of size (22.5 cm × 11.25 cm × 8.75 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

Answer 1

(c) 11200
Volume of wall = $270\times 300\times 350{\mathrm{cm}}^3$
$\frac{1}{8}\mathrm{th}$ of the wall is covered with mortar.
So,
Volume of the wall filled with bricks$=\left(\frac{7}{8}\times 270\times 300\times 350\right){\text{cm}}^3$
Volume of each brick$=\left(\frac{225}{10}\times \frac{1125}{100}\times \frac{875}{100}\right){\text{cm}}^3$
$=\left(\frac{9\times 225\times 35}{32}\right){\text{cm}}^3$

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.