How many cubic yards of concrete are needed for a slab that measures 30 feet by 40 feet by 6 inches thick?
Correct Answer
D) 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: 27.8 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 C: 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.
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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