A residential building in Michigan has a roof area of 2,400 square feet. If the area receives 30 inches of annual rainfall, how many gallons of water could potentially be collected annually? (1 inch of rain on 1 sq ft = 0.623 gallons)
Correct Answer
C) 44,856 gallons
Water collection = Roof area × Rainfall × Conversion factor = 2,400 sq ft × 30 inches × 0.623 gallons = 44,856 gallons annually.
Why This Is the Correct Answer
Option C is correct. The calculation is: Water collected = Roof area × Annual rainfall × Conversion factor = 2,400 sq ft × 30 inches × 0.623 gal/(sq ft·inch) = 44,856 gallons. All three values are multiplied together using the provided conversion factor.
Why the Other Options Are Wrong
Option A: 38,844 gallons
38,844 gallons is incorrect. This result suggests an arithmetic error—possibly using a different conversion factor or only multiplying two of the three values. For example, 2,400 × 0.623 × 26 ≈ 38,844, using 26 inches instead of 30 inches.
Option B: 52,200 gallons
52,200 gallons is incorrect. This may result from using a rounded conversion factor (e.g., 0.725 instead of 0.623) or from a different combination of variables. 2,400 × 30 × 0.725 ≈ 52,200.
Option D: 72,000 gallons
72,000 gallons is incorrect. This likely results from ignoring the conversion factor entirely and simply multiplying 2,400 × 30 = 72,000. This treats each unit of rainfall as one gallon per square foot, which overstates actual collection by about 60%.
Memory Technique
The formula is Area × Rainfall × 0.623. Think of 0.623 as 'about 62%'—you only capture about 62% of rainfall as usable gallons per square foot per inch (due to the unit conversion from cubic inches to gallons). Write out the full equation before plugging in numbers to avoid missing any factor.
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