Question

A cistern, internally measuring $150cm\times 120cm\times 100cm$, has $129600c{m}^3$ of water in it. Porous bricks are placed in the water until the cistern is full to the brim. Each brick absorbs one-seventeenth of its own volume of water. How many bricks can be put in without overflowing the water, each being$22.5cm\times 7.5cm\times 6.5cm$ ?

Answer 1

Volume of Cistern$=lXbXh$

$=150\times 120\times 110=1980000c{m}^3$

Volume of Water $=129600c{m}^3$

Empty space left in Cistern $=1980000-129600=1850400c{m}^3$

Volume of Brick$=l\times b\times h=22.5\times 7.5\times 6.5=1096.88c{m}^3$

Volume of $n$Bricks$=(1096.88\times n)c{m}^3$

Volume absorbed by each brick $=\frac{1}{17}th(volumeofbrick)$

$=\frac{1}{17}\times 1096.88c{m}^3=64.522c{m}^3$

Then, Volume absorbed by $n$bricks$=64.522\times n$

$\text{Volume of brick = Empty space left in Cistern + volume absorbed by bricks}$

$=1096.88\times n=1850400+64.522\times n$

$$\begin{gathered} =n\times (1096.88-64.522)=1850400 \\ =n=1792.40 \\ =n=1792 \end{gathered}$$

Hence the number of bricks$=1792$