Question

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

Answer 1

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

$\therefore$ Volume of the wall $=(400\times 1500\times 30)c{m}^3=18000000c{m}^3$

Given that $\frac{1}{12}$ volume of wall consists of mortar.

Volume of the wall consisting of mortar $=\frac{18000000}{12}=1500000c{m}^3$

So, Volume of wall consisting of bricks $=18000000-1500000=16500000c{m}^3$.

Dimensions of brick, $l=20cm,$ $b=12.5cm,$ $h=7.5cm.$

Volume of each brick $=l\times b\times h=(20\times 12.5\times 7.5)c{m}^3=1875c{m}^3$

Now, the number of bricks in the wall $=\frac{\text{Volume of the wall consisting of bricks}}{\text{Volume of one brick}}$

Number of bricks in wall $=\frac{16500000}{1875}=8800.$

Thus, there are $8800$ bricks in the wall.

Hence, the required number of bricks is $8800.$