How many cubic yards of concrete are needed for a foundation wall that is 100 feet long, 8 inches thick, and 4 feet high?
Correct Answer
C) 9.88 cubic yards
Volume = 100 ft × (8/12) ft × 4 ft = 266.67 cubic feet. Converting to cubic yards: 266.67 ÷ 27 = 9.88 cubic yards.
Why This Is the Correct Answer
The correct answer is A because we must first convert all measurements to the same units (feet), then calculate volume in cubic feet, and finally convert to cubic yards. The 8-inch thickness must be converted to feet (8÷12 = 0.667 ft), then multiply length × width × height (100 × 0.667 × 4 = 266.67 cubic feet). Finally, divide by 27 to convert cubic feet to cubic yards (266.67 ÷ 27 = 9.88 cubic yards).
Why the Other Options Are Wrong
Option A: 11.85 cubic yards
This answer likely results from an error in unit conversion or using incorrect dimensions in the calculation, possibly forgetting to convert inches to feet properly.
Option B: 12.96 cubic yards
This answer suggests a calculation error, possibly multiplying by an incorrect conversion factor or making an arithmetic mistake in the volume calculation.
Option D: 14.81 cubic yards
This answer is too high and likely results from failing to convert the 8 inches to feet, or using an incorrect conversion factor between cubic feet and cubic yards.
Memory Technique
Remember '27 to the sky' - there are 27 cubic feet in 1 cubic yard (3×3×3=27). Also remember 'inches to feet, divide by 12 neat' for converting inches to feet.
Reference Hint
Look up concrete volume calculations in the construction materials chapter, specifically the section on unit conversions and cubic yard calculations.
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