A wall 15 m long, 30 cm wide and 4 m high is made of bricks, each measuring (22 cm × 12.5 cm × 7.5 cm).

Question:

A wall $15 \mathrm{~m}$ long, $30 \mathrm{~cm}$ wide and $4 \mathrm{~m}$ high is made of bricks, each measuring $(22 \mathrm{~cm} \times 12.5 \mathrm{~cm} \times 7.5 \mathrm{~cm})$. If $\frac{1}{12}$ of the total volume of the wall consists of mortar, how many bricks are there in the wall?

Solution:

Length of the wall = 15 m = 1500 cm
Breadth of the wall = 30 cm
Height of the wall = 4 m = 400 cm

Volume of wall $==1500 \times 30 \times 400 \mathrm{~cm}^{3}=18000000 \mathrm{~cm}^{3}$

Now, volume of each brick $=22 \times 12.5 \times 7.5 \mathrm{~cm}^{3}$

$=2062.5 \mathrm{~cm}^{3}$

Also, volume of the mortar $=\frac{1}{12} \times$ volume of the wall

$=\frac{18000000}{12}=1500000 \mathrm{~cm}^{3}$

Total volume of the bricks in the wall = volume of the wall − volume of the mortar

= (18000000 − 1500000) cm3= 16500000 cm3

$\therefore$ Number of bricks $=\frac{\text { volume of bricks }}{\text { volume of one brick }}=\frac{16500000}{2062.5}=8000$ bricks

 

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