Question 1149973
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.