A site plan shows existing grade at elevation 100.0 and proposed grade at elevation 102.5. If the lot area to be filled is 5,000 square feet, how many cubic yards of fill material are needed?
Correct Answer
B) 463 cubic yards
The fill depth is 2.5 feet (102.5 - 100.0). Volume = 5,000 sq ft × 2.5 ft = 12,500 cubic feet. Converting to cubic yards: 12,500 ÷ 27 = 463 cubic yards (rounded).
Why This Is the Correct Answer
This is a straightforward earthwork calculation requiring three steps: finding the fill depth, calculating volume in cubic feet, and converting to cubic yards. The fill depth is 2.5 feet (102.5 - 100.0), which when multiplied by the area gives 12,500 cubic feet. Dividing by 27 (cubic feet per cubic yard) yields 463 cubic yards.
Why the Other Options Are Wrong
Option A: 521 cubic yards
This answer likely results from an error in the conversion factor or rounding, possibly using an incorrect divisor or making arithmetic mistakes in the final conversion step.
Option C: 625 cubic yards
This answer represents the volume if calculated in cubic feet but then mistakenly labeled as cubic yards, forgetting the essential conversion step from cubic feet to cubic yards.
Memory Technique
Remember '27 CUBES' - picture a 3×3×3 cube made of 27 smaller cubes to visualize that 27 cubic feet equals 1 cubic yard. For earthwork: Depth × Area ÷ 27 = cubic yards.
Reference Hint
Look up earthwork calculations and volume conversions in the construction mathematics or site work sections of your reference materials, typically found in general contracting handbooks under excavation and grading.
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