SOLUTION: A company is to construct a parking bay whose area is 135 square meters. it is to be covered with a concrete slab of uniform thickness of 0.15 meters. to make the slab,cement, ball

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Question 1149973: A company is to construct a parking bay whose area is 135 square meters. it is to be covered with a concrete slab of uniform thickness of 0.15 meters. to make the slab,cement, ballast and sand are to be mixed so that their masses are in the ratio 1:4:4 the mass of 1 cubic meter of dry slab is 2,500 kilogram
A) calculate i)the volume of the slab
ii)the mass of the dry slab
iii)the mass of cement to be used
B)If one bag of cement is 50 kilogram, find the number of bags to be purchased
C) if a lorry carries 7 tonnes of sand, calculate the number of lorries of sand to be purchased.
Answer by Theo(13342) About Me  (Show Source):
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the parking bay area is 135 square meters.
it is to be covered by a concrete slab of .15 meters of uniform thickness.
to make the slab, cement, ballast, and sand are to be mixed in the ratios of 1:4:4.
the mass of 1 cubic meter of dry slab is 2500 kilograms.

the volume of the slab is .15 * 135 = 20.25 cubic meters.

the mass of the dry slab is 20.25 cubic meters * 2500 kilograms per cubic meter = 50625 kilograms.

since the masses of cement:ballast:sand are in the ratio of 1:4:4, then the mass of the cement is equal to 1/9 * the mass of the mixture = 5625 kilograms.
with each bag cement weighing 50 kilograms, the number of bags of cement require are 5625 / 50 = 112.5

1 tonne = 1 metric ton = 1000 kilograms.
1 lorry = 7 tonnes = 7000 kilograms.
number of kilograms of sand is equal to 4/9 * 50625 = 22500 kilograms.
number of lorries required is 22500 / 7000 = 3.214285714.

the ratio of cement to ballast is 5625 / 22500 * (1/5625) / (1/5625) = 1/4.
the ratio of ballast to sand is 22500 / 22500 * (1/5625) / (1/5625) = 4/4.
the ratio of cement to total is equal to 1 / (1 + 4 + 4) = 1/9.
the ratio of ballast to total is equal to 4 / (1 + 4 + 4) = 4/9.
the ratio of sand to total is equal to 4 / (1 + 4 + 4) = 4/9.
the ratios are by mass, therefore:
the mass of the cement is 1/9 * 50625 = 5625 kilograms.
the mass of the ballast is 4/9 * 50625 = 22500 kilograms.
the mass of the sand is 4/9 * 50625 = 22500 kilograms.
the sum of all 9 parts is equal to 50625.

that's what i get.