A rectangular lot measures 150 feet by 200 feet. If the lot is located in a flood zone requiring 2 feet of fill, and fill costs $8 per cubic yard, what is the cost of fill for the entire lot?
Correct Answer
B) $22,222
Lot area: 150 × 200 = 30,000 sq ft. Volume of fill: 30,000 × 2 = 60,000 cubic feet. Convert to cubic yards: 60,000 ÷ 27 = 2,222.22 cubic yards. Cost: 2,222.22 × $8 = $17,778. The answer should be $17,778, making option A correct.
Why This Is the Correct Answer
Option A ($17,778) is correct based on the step-by-step calculation. First, calculate the lot area: 150 × 200 = 30,000 square feet. Then determine the volume of fill needed: 30,000 sq ft × 2 feet = 60,000 cubic feet. Convert to cubic yards by dividing by 27 (since 1 cubic yard = 27 cubic feet): 60,000 ÷ 27 = 2,222.22 cubic yards. Finally, multiply by the cost per cubic yard: 2,222.22 × $8 = $17,778.
Why the Other Options Are Wrong
Option C: $24,000
Option C ($24,000) likely results from incorrectly calculating the cubic yards as 3,000 instead of 2,222.22, possibly by using an incorrect conversion factor or rounding errors in the intermediate steps.
Option D: $26,667
Option D ($26,667) appears to result from significant calculation errors, possibly in the area calculation or unit conversion, leading to an overestimate of approximately 50% above the correct answer.
The 27 Cube Rule
Remember '27 CUBES': 27 Cubic feet = 1 Cubic Yard. Visualize a 3×3×3 cube where each small cube is 1 foot - that's 27 cubic feet making 1 cubic yard.
How to use: When you see any volume calculation question, immediately think '27 CUBES' to remember the conversion factor. Always convert cubic feet to cubic yards by dividing by 27 before applying the cost per cubic yard.
Exam Tip
Write out each step clearly: Area → Volume in cubic feet → Volume in cubic yards → Total cost. Double-check that you're dividing by 27, not multiplying, when converting cubic feet to cubic yards.
Common Mistakes to Avoid
- -Forgetting to convert cubic feet to cubic yards before applying the cost
- -Using the wrong conversion factor (multiplying by 27 instead of dividing)
- -Calculating area incorrectly or using wrong dimensions
Concept Deep Dive
Analysis
This question tests the appraiser's ability to calculate site improvement costs, specifically fill material costs for flood zone compliance. The problem requires converting between different units of measurement (square feet to cubic feet to cubic yards) and applying cost per unit calculations. This type of calculation is essential for determining the cost approach to value, where site preparation costs directly impact the overall property valuation. The question also demonstrates the practical reality that properties in flood zones often require elevation improvements to meet building codes and insurance requirements.
Background Knowledge
Appraisers must understand volume calculations and unit conversions when estimating site improvement costs for the cost approach. Fill material is typically sold by the cubic yard, requiring conversion from square footage and depth measurements to cubic yards (27 cubic feet = 1 cubic yard).
Real-World Application
In flood-prone areas, appraisers frequently encounter properties requiring fill to meet FEMA elevation requirements. These costs directly impact the site value and overall cost approach calculations, making accurate volume and cost calculations essential for proper valuation.
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