A contractor is estimating concrete for a foundation that measures 120 feet by 80 feet with a thickness of 8 inches. How many cubic yards of concrete are needed?
Correct Answer
C) 237 cubic yards
Calculate: 120' × 80' × (8/12)' = 6,400 cubic feet. Convert to yards: 6,400 ÷ 27 = 237 cubic yards. Always convert thickness from inches to feet before calculating.
Why This Is the Correct Answer
Option C is correct because the calculation properly converts all measurements to the same units before computing volume. The thickness of 8 inches must be converted to feet (8/12 = 0.667 feet) before multiplying with the length and width. The resulting cubic feet is then correctly converted to cubic yards by dividing by 27, since there are 27 cubic feet in one cubic yard.
Why the Other Options Are Wrong
Option A: 178 cubic yards
This answer is too low, likely resulting from an error in unit conversion or calculation. The contractor may have made an error in converting inches to feet or cubic feet to cubic yards.
Option B: 213 cubic yards
This answer is close but still incorrect, suggesting a minor calculation error or rounding mistake in the conversion process.
Option D: 284 cubic yards
This answer is too high, possibly from failing to convert the 8-inch thickness to feet before calculating, or from using an incorrect conversion factor.
Memory Technique
Remember '27 to the sky' - there are 27 cubic feet in a cubic yard (3×3×3). Always convert thickness from inches to feet by dividing by 12 before calculating concrete volume.
Reference Hint
Florida Building Code, Chapter 19 - Concrete, or construction mathematics reference sections covering volume calculations and unit conversions
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