Question

A cistern, internally measuring 150 cm × 120 cm × 110 cm, has 129600 cm³ 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 × 7.5 cm × 6.5 cm?

Answer 1

Volume of cistern = 150 × 120 × 110

= 1980000 cm³

Volume to be filled in cistern = 1980000 − 129600

= 1850400 cm³

Let n numbers of porous bricks were placed in the cistern.

Volume of n bricks = n × 22.5 × 7.5 × 6.5

= 1096.875n

As each brick absorbs one-seventeenth of its volume, therefore, volume absorbed by these bricks 

= n/17(1096.875)

${\displaystyle 1850400+\frac{n}{17}\left(1096.875\right)=\left(1096.875\right)n}$

${\displaystyle 1850400=\frac{16n}{17}\left(1096.875\right)}$

n = 1792.41

Therefore, 1792 bricks were placed in the cistern.