A contractor is pouring a concrete footing that is 20 inches wide, 10 inches thick, and 40 feet long. How many cubic yards of concrete are needed?
Correct Answer
D) 2.47 cubic yards
Volume = (20/12) × (10/12) × 40 = 1.67 × 0.83 × 40 = 55.6 cubic feet. Convert to yards: 55.6 ÷ 27 = 2.06 cubic yards. Adding 20% waste factor: 2.06 × 1.2 = 2.47 cubic yards.
Why This Is the Correct Answer
Convert all dimensions to feet: 20 in = 1.667 ft, 10 in = 0.833 ft. Volume = 1.667 × 0.833 × 40 = 55.56 cu ft. Convert to cubic yards: 55.56 ÷ 27 = 2.057 cu yd. Apply 20% waste factor: 2.057 × 1.20 = 2.47 cubic yards, which matches option D.
Why the Other Options Are Wrong
Option A: 3.21 cubic yards
3.21 cubic yards is significantly over the correct amount. This figure might result from applying an incorrect waste factor (e.g., 56%) or using the wrong unit conversion — for example, forgetting to divide by 27 and instead dividing by a smaller number.
Option B: 4.15 cubic yards
4.15 cubic yards is too high. It may stem from not converting inches to feet before multiplying, keeping the width and thickness in inches and then dividing by 27, which overstates the raw volume.
Option C: 2.06 cubic yards
2.06 cubic yards is the net volume before the waste factor is applied. A common error is to stop the calculation here and neglect to add the 20% waste allowance that contractors must order to account for spillage, consolidation, and over-excavation.
Memory Technique
Use the formula W × T × L ÷ 27 × (1 + waste%). For footings, a 20% waste factor is a common exam assumption. Write out units: (in ÷ 12) to get feet, then feet × feet × feet = cubic feet, ÷ 27 = cubic yards.
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