the water until the cistern is full to the brim.Each brick absorbs 1/17th of its own volume of water.How many bricks can be put in without overflowing the water,Each brick being 22.5cm*7.5cm*6.5cm.
A cistern internally measuring 150cm* 120cm* 110cm has 129600 cub.cm water in it.Porous bricks are placed in?
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Verified answer
volume of cistern = Vc = 150* 120* 110 = 1980000cm³
volume water = Vw = 129600cm³
volume empty = Ve = Vc - Vw = 1850400cm³
volume brick = Vb = 22.5*7.5*6.5 = 1096.875cm³
each brick uses up it's own volume less 1/17, so it only uses up 16/17 of its volume (ie volume of 16Vb/17 each)
so if N is the maximum number of bricks, you'll have
Ve = N(16Vb/17)
so
N = 17Ve/16Vb = 1792.4 ≈ 1792 bricks
,.,..,..
1792 bricks worked out as under.
Volume of cistern = 150cm* 120cm* 110cm = 1980000 cc
Volume of each brick = 22.5cm*7.5cm*6.5cm = 1096.875 cc
Water absorbed by each brick = 1096.875/17 = 156.7cc
Let x = no. of bricks used
Then 129600 - 64.52 x = 1980000 - 1096.875 x
=> 1032.355 x = 1850400
=> x = 1792.4 Hence,
a maximum of 1792 bricks can be put without water overflowing.
[I realized my arithmetical error after seeing the answer of Black Wolf and corrected the arithmetical error. His method is a bit superior.]
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