Question

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

Answer 1

Length of the wall $=15m=1500cm$
Breadth of the wall $=30cm$
Height of the wall $=4m=400cm$
Volume of wall $=1500\times 30\times 400c{m}^3=18000000c{m}^3$
Now, volume of each brick $=22\times 12.5\times 7.5c{m}^3=2062.5c{m}^3$
Also, volume of the mortar $=\frac{1}{12}\times$ volume of the wall
$=\frac{18000000}{12}=1500000c{m}^3$
Total volume of the bricks in the wall $=$ volume of the wall $-$ volume of the mortar
$=(18000000-1500000)c{m}^3=16500000c{m}^3$
$\therefore$ Number of bricks $=\frac{\text{volume of bricks}}{\text{volume of one brick}}=\frac{16500000}{2062.5}=8000$ bricks