How many cubic yards of concrete are needed for a foundation wall that is 100 feet long, 8 inches thick, and 6 feet high?
Correct Answer
B) 14.8 cubic yards
Volume = 100' × (8/12)' × 6' = 400 cubic feet. Converting to cubic yards: 400 ÷ 27 = 14.8 cubic yards.
Why This Is the Correct Answer
To find concrete volume, we must first calculate the volume in cubic feet using consistent units, then convert to cubic yards. The wall dimensions are 100 feet long × 8/12 feet thick (converting inches to feet) × 6 feet high = 400 cubic feet. Since there are 27 cubic feet in one cubic yard, we divide 400 by 27 to get 14.8 cubic yards.
Why the Other Options Are Wrong
Option A: 22.2 cubic yards
This answer of 17.8 cubic yards suggests an error in the calculation, possibly from incorrectly converting the 8-inch thickness or making an arithmetic mistake in the division by 27.
Option C: 17.8 cubic yards
This answer of 22.2 cubic yards is too high and likely results from a calculation error, possibly from not properly converting the 8 inches to feet or making an error in the final division.
Option D: 400 cubic feet
While 400 cubic feet is the correct intermediate calculation, the question asks for cubic yards, not cubic feet, making this answer incomplete and in the wrong units.
Memory Technique
Remember '27 to fly' - there are 27 cubic feet in a cubic yard (3×3×3), and concrete calculations need to 'fly' from cubic feet to cubic yards for ordering.
Reference Hint
Look up concrete volume calculations and unit conversions in the construction materials or estimating chapter of your reference manual.
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