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Answer :
The solid volume of concrete per sack of cement is approximately 6.02 cubic feet, considering a water-cement ratio of 0.52, mix ratio of 1:2.1:2.3 for sand and coarse aggregate, and accounting for potential air content.
Find the solid volume of concrete per sack of cement:
1: Calculate the water volume per sack of cement.
We know the water-cement ratio is 0.52. Let W be the volume of water and C be the volume of cement in one sack. Then, W = 0.52C.
2: Express the volumes of sand and coarse aggregate in terms of cement volume.
We know the mix ratio is 1:2.1:2.3. This means for every 1 part cement, there are 2.1 parts sand and 2.3 parts coarse aggregate.
Therefore, the volume of sand (S) is 2.1C and the volume of coarse aggregate (G) is 2.3C.
3: Account for air content.
We need to consider the air content (let's say it's A) which will reduce the total solid volume.
4: Total volume equation.
The total volume (V) of the concrete mix per sack of cement is the sum of all components: V = C + W + S + G - A.
5: Substitute and simplify.
Substitute the expressions for W, S, and G obtained in Step 2: V = C + 0.52C + 2.1C + 2.3C - A.
Combine like terms: V = 6.02C - A.
6: Convert cement volume to sack weight.
We know a sack of cement weighs 94 lbs. We need to find the volume of cement per sack (C) in cubic feet to plug it into the equation.
Density of cement varies, but a typical value is 94 lbs/ft^3. Therefore, C = 94 lbs / 94 lbs/ft^3 = 1 ft^3.
7: Plug values and calculate solid volume.
Assuming no air content (A = 0), V = 6.02(1 ft^3) - 0 = 6.02 ft^3.
Therefore, the solid volume of concrete obtained per sack of cement is approximately 6.02 cubic feet.
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