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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?

Solution:

Let's construct a diagram according to the given 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?

Internal volume of cistern = (Volume of water in the cistern - Volume of water absorbed by bricks) + Volume of bricks

Internal volume of cistern = Volume of water in cistern - 1/17 × Volume of bricks + Volume of bricks

Hence,

Internal volume of cistern = Volume of water in the cistern + 16/17 volume of bricks

Since the dimensions of the cistern and the brick are known which are cuboidal in shape, we will find the volume by using formula;

Volume of the cuboid = lbh

where l, b and h are length, breadth and height of the cuboid respectively.

Internal volume of the cistern = 150 cm × 120 cm × 110 cm = 1980000 cm³

Volume of water in the cistern = 129600 cm³

Volume of one brick = 22.5 cm × 7.5 cm × 6.5 cm = 1096.875 cm³

Let the required number of bricks be ‘x’

Volume of x bricks = x × 1096.875 cm³

Internal volume of cistern = Volume of water in the cistern + 16/17 volume of x bricks

1980000 cm³ = 129600 cm³ + 16/17 × x × 1096.875 cm³

x = [(1980000 cm³ - 129600 cm³) × 17] / (16 × 1096.875) cm³

= (1850400 cm³ × 17) / (16 × 1096.875 cm³)

= 1792.41

Since the number of bricks should be a whole number, whole part of x should be considered as the answer. Rounding off x to the next whole number should not be considered as it will lead to overflowing of tank, if that extra fractional part is added to the cistern.

Therefore, the number of bricks which can be put in the cistern without overflowing the water is 1792.

☛ Check: NCERT Solutions Class 10 Maths Chapter 13

Video 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. 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?

NCERT Solutions for Class 10 Maths Chapter 13 Exercise 13.5 Question 3

Summary:

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. The number of bricks which can be put in the cistern without overflowing the water with each brick being 22.5 cm × 7.5 cm × 6.5 cm is 1792.

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