A cistern, internally measuring 150 cm × 120 cm × 100 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 being 22.5 cm × 7.5 cm × 6.5 cm?

Given

Length of Cistern (L) = 150 cm

Breadth of Cistern (W) = 120 cm

Height of Cistern (H) = 110 cm

Length of Brick (l) = 22.5 cm

Breadth of Brick (w) = 7.5 cm

Height of Brick (h) = 6.5 cm

Find out

We have to find the number of bricks

Solution

Volume of Cistern = l X b X h

= 150×120×110

= 1980000 cm3

Volume of Water = 129600 cm3

Empty space left in Cistern = 1980000-129600

= 1850400 cm3

Volume of Brick = l×b×h

= 22.5×7.5×6.5

= 1096.88 cm3

Volume of n Bricks = 1096.88×n cm3

Volume absorbed by each brick = (1/17)th (volume of brick)

= 1/17×1096.88 cm3

= 64.522 cm3

Then, Volume absorbed by n bricks = 64.522×n

Volume of brick = Empty space left in Cistern + volume absorbed by bricks

1096.88×n = 1850400 + 64.522×n

n×(1096.88-64.522) = 1850400

n = 1792.40

n = 1792 

Answer

The number of bricks=1792

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