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NCERT Solutions Class 10 Mathematics Solutions for Surface Areas and Volumes - Exercise 13.5 in Chapter 13 - Surface Areas and Volumes

Question 6 Surface Areas and Volumes - Exercise 13.5

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?

Answer:

Given that the dimension of the cistern = 150 × 120 × 110

So, volume = 1980000 cm3

Volume to be filled in cistern = 1980000 – 129600

= 1850400 cm3

Now, let the number of bricks placed be “n”

So, volume of n bricks will be = n×22.5×7.5×6.5

Now as each brick absorbs one-seventeenth of its volume, the volume will be

= n/(17)×(22.5×7.5×6.5)

For the condition given in the question,

The volume of n bricks has to be equal to volume absorbed by n bricks + Volume to be filled in cistern

Or, n×22.5×7.5×6.5 = 1850400+n/(17)×(22.5×7.5×6.5)

Solving this we get,

n = 1792.41

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