How many cubic yards of concrete are needed for a slab that measures 30 feet by 40 feet by 6 inches thick?
Correct Answer
B) 22.2 cubic yards
Volume = 30 × 40 × 0.5 = 600 cubic feet. Convert to cubic yards: 600 ÷ 27 = 22.2 cubic yards. Always convert thickness to feet (6 inches = 0.5 feet) before calculating.
Why This Is the Correct Answer
Option B is correct because the calculation properly converts all measurements to the same units before computing volume. The thickness of 6 inches must be converted to 0.5 feet to match the length and width units. The volume calculation (30 × 40 × 0.5 = 600 cubic feet) is then correctly converted to cubic yards by dividing by 27, yielding 22.2 cubic yards.
Why the Other Options Are Wrong
Option A: 18.5 cubic yards
This answer is too low, likely resulting from an error in unit conversion or calculation. It may come from incorrectly using 6 inches as 6 feet in the calculation or making an arithmetic error in the conversion process.
Option C: 24.7 cubic yards
This answer is too high, possibly from using incorrect thickness conversion (like 6 inches = 0.6 feet instead of 0.5 feet) or making an error in the cubic feet to cubic yards conversion factor.
Option D: 27.8 cubic yards
This answer significantly overestimates the concrete needed, likely from a major unit conversion error such as forgetting to convert inches to feet entirely or using an incorrect conversion factor when changing cubic feet to cubic yards.
Memory Technique
Remember 'FEET FIRST, THEN 27' - always convert everything to feet before calculating, then divide by 27 to get cubic yards. Also remember: 1 cubic yard = 3×3×3 = 27 cubic feet.
Reference Hint
Look up concrete calculations and volume conversions in the construction materials chapter or appendix containing unit conversion tables.
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