A cistern, internally measuring 150 cm x 120 cm x 110 cm, has 129600 cu.cm 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?

Explanation

`"Total volume of the cistern "=(150 xx 120 xx 110) cm^(3)`
`=19080000cm^(3)`
`"Volume of the water in the cistern "=12960 cm^(3)`.
`"Volume of the empty space in the cistern"`
`=(1980000-129600) cm ^(3)=1850400 cm^(3)`.
`"Total volume of each brick"=(22.5xx8=7.5xx6.5)cm^(3)`
`=1096.875 cm^(3)`.
Since each brick absorbs water equal to `1/10` of its own volume,
so the effective volume of each brick may be taken as `(1-1/17)"i.e.,"16/17` of its actual volume.
So, the effective volume of each brick `= (16/17xx1096.875) cm^(3)`.
`:." required number of bricks"`
`=("volume of emply space in the cistern")/("effective volume of ach brick")`
`=(1850400)/(16/17xx1096.875)=(17xx1850400)/(16xx1096.875)`
`=(17xx1850400)/(17550)=1792.41=1792("approx").`