A structural drawing shows a concrete footing detail with dimensions of 3'-0" x 3'-0" x 1'-6" deep. If 25 such footings are required, what is the total cubic yards of concrete needed?
Correct Answer
A) 12.5 cubic yards
Each footing: 3' × 3' × 1.5' = 13.5 cubic feet. For 25 footings: 13.5 × 25 = 337.5 cubic feet. Converting to cubic yards: 337.5 ÷ 27 = 12.5 cubic yards.
Why This Is the Correct Answer
The calculation correctly follows the three-step process for concrete volume calculations: first finding the volume of one footing (3' × 3' × 1.5' = 13.5 cubic feet), then multiplying by the quantity needed (13.5 × 25 = 337.5 cubic feet), and finally converting from cubic feet to cubic yards by dividing by 27 (337.5 ÷ 27 = 12.5 cubic yards). This systematic approach ensures accurate concrete quantity estimation for ordering purposes.
Why the Other Options Are Wrong
Option B: 25 cubic yards
This answer suggests a significant calculation error, possibly from incorrectly converting units or using the wrong conversion factor, resulting in an overestimate that could lead to substantial material waste and cost overruns.
Option C: 42.5 cubic yards
This answer likely results from an error in the conversion factor or calculation steps, possibly using an incorrect divisor when converting from cubic feet to cubic yards or making an arithmetic mistake in the multiplication phase.
Option D: 15.6 cubic yards
This answer appears to come from simply using the number of footings (25) without performing any volume calculations, completely ignoring the dimensional requirements of each individual footing.
Memory Technique
Remember '27 to fly' - it takes 27 cubic feet to make 1 cubic yard 'fly' off your material list. Also, always work in the sequence: Length × Width × Height × Quantity ÷ 27.
Reference Hint
Florida Building Code, Chapter 19 - Concrete, or construction estimating references covering concrete volume calculations and unit conversions
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