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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. - CBSE Class 10 - Mathematics

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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?

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.

  Is there an error in this question or solution?

APPEARS IN

 NCERT Solution for Mathematics Textbook for Class 10 (2019 to Current)
Chapter 13: Surface Areas and Volumes
Ex. 13.40 | Q: 3 | Page no. 258

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Solution 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. Concept: Surface Areas and Volumes Examples and Solutions.
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