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. - Mathematics

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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?

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Solution

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)

`1850400 + n/17 (1096.875) = (1096.875)n`

`1850400 = (16n)/17(1096.875)`

n = 1792.41

Therefore, 1792 bricks were placed in the cistern.

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Chapter 13: Surface Areas and Volumes - Exercise 13.5 [Page 258]

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NCERT Mathematics Class 10
Chapter 13 Surface Areas and Volumes
Exercise 13.5 | Q 3 | Page 258

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