When calculating concrete volume for a foundation wall that is 100 feet long, 8 inches thick, and 4 feet high, how many cubic yards of concrete are required?
Correct Answer
A) 9.88 cubic yards
Volume calculation: 100 ft × (8/12) ft × 4 ft = 266.67 cubic feet. Converting to cubic yards: 266.67 ÷ 27 = 9.88 cubic yards. Accurate concrete volume calculations are essential for proper material ordering and cost estimation in California construction projects.
Why This Is the Correct Answer
The calculation: Length × Width × Height = 100 ft × (8 ÷ 12) ft × 4 ft = 100 × 0.667 × 4 = 266.67 cubic feet. Convert to cubic yards: 266.67 ÷ 27 = 9.88 cubic yards. This is the correct result because all dimensions are properly converted to the same unit (feet) before multiplying, and the final conversion divides by 27 (the number of cubic feet in one cubic yard).
Why the Other Options Are Wrong
Option B: 8.64 cubic yards
8.64 cubic yards results from an error in converting the wall thickness. A common mistake is dividing 8 inches by 12 incorrectly or rounding 0.667 down to 0.6, giving 100 × 0.6 × 4 = 240 cubic feet ÷ 27 = 8.89, or from using a slightly different rounding approach. This answer reflects a dimensional conversion error.
Option C: 10.67 cubic yards
10.67 cubic yards results from converting the 8-inch thickness to feet as 8/9 = 0.889 instead of 8/12 = 0.667, or from another arithmetic error that inflates the volume. This overestimates the actual concrete needed.
Option D: 7.41 cubic yards
7.41 cubic yards significantly underestimates the volume. This could result from using 8 inches as 8/12 of a yard (0.222 yards) instead of 8/12 of a foot, or from another unit confusion. Always ensure all dimensions are in the same unit before multiplying.
Memory Technique
Use the formula: V (cy) = (L × W × H) ÷ 27. The key anchor is '27 cubic feet per cubic yard.' Think of a cube that is 3 feet on each side: 3 × 3 × 3 = 27. Always convert all measurements to feet first, then divide by 27.
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