Question

A cistern, internally measuring $150$ cm x $120$ cm x $110$ cm, has $129600$ cm ${}^3$ 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 brick being $22.5$ cm x $7.5$cm x $6.5$ cm

Answer 1

Volume of cistern $=150\times 120\times 110$
$=1980000$ cm${}^3$

Volume to be filled in cistern $=\frac{1980000}{129600}$
$=1850400$ cm ${}^3$

Let $x$ numbers of porous bricks were placed in the cistern.
Volume of $x$ bricks = $x\times 22.5\times 7.5\times 6.5$
$=1096.875x$

As each brick absorbs one-seventeenth of its volume, therefore, volume absorbed by these bricks
$=\frac{x}{17}\left(1096.875\right)$

$\Rightarrow 1850400+\frac{x}{17}\left(1096.875\right)=\left(1096.875\right)x$

$\Rightarrow 1850400=\frac{16x}{17}\left(1096.875\right)$

$x=1792.41$

Therefore, $1792$ bricks were placed in the cistern.