A building measures 40 feet by 60 feet and has a height of 12 feet. What is the total volume in cubic feet?
Correct Answer
B) 28,800 cubic feet
Volume is calculated as length × width × height. 40 feet × 60 feet × 12 feet = 28,800 cubic feet.
Why This Is the Correct Answer
Option B is correct because volume is calculated using the formula: Volume = Length × Width × Height. Given the building dimensions of 40 feet × 60 feet × 12 feet, the calculation is straightforward: 40 × 60 × 12 = 28,800 cubic feet. This represents the total three-dimensional space contained within the building structure. The calculation must include all three dimensions to properly determine the volumetric capacity of the structure.
Why the Other Options Are Wrong
Option A: 2,400 cubic feet
Option A (2,400 cubic feet) represents only the floor area calculation (40 × 60 = 2,400 square feet) without accounting for the height dimension, making it a two-dimensional rather than three-dimensional measurement.
Option C: 7,200 cubic feet
Option C (7,200 cubic feet) appears to be the result of multiplying only two dimensions by the height (60 × 12 = 720, then somehow getting to 7,200), representing an incomplete or incorrect calculation that doesn't use all three dimensions properly.
Option D: 14,400 cubic feet
Option D (14,400 cubic feet) is exactly half of the correct answer, suggesting a calculation error where perhaps only two dimensions were multiplied correctly (40 × 60 = 2,400) and then multiplied by 6 instead of 12, or some other computational mistake.
LWH Box Method
Remember 'LWH' - Length × Width × Height - by visualizing a cardboard box and thinking 'Long Ways High.' Picture yourself measuring a box: first the length (how long), then the width (how wide), then the height (how high).
How to use: When you see a volume question, immediately write 'L × W × H =' and fill in the three dimensions given in the problem. Visualize the building as a simple rectangular box to ensure you're using all three measurements.
Exam Tip
Always double-check that you're using all three dimensions in volume calculations - length, width, AND height. Write out the formula first, then substitute the numbers to avoid missing a dimension.
Common Mistakes to Avoid
- -Forgetting to include the height dimension and calculating only area
- -Mixing up which measurements represent length, width, and height
- -Making arithmetic errors when multiplying three numbers together
Concept Deep Dive
Analysis
This question tests the fundamental geometric concept of calculating volume for rectangular structures, which is essential in real estate appraisal for determining building capacity, storage space, and certain valuation methods. Volume calculations are particularly important when appraising warehouses, storage facilities, or when using cost approaches that consider cubic footage. The question requires understanding that volume is a three-dimensional measurement requiring length, width, and height. This basic mathematical skill forms the foundation for more complex appraisal calculations involving building measurements and space analysis.
Background Knowledge
Volume calculations require understanding three-dimensional geometry and the basic formula Volume = Length × Width × Height for rectangular structures. In real estate appraisal, volume measurements are used for specific property types and valuation approaches, particularly when space capacity is a key value driver.
Real-World Application
Appraisers use volume calculations when valuing warehouses, storage facilities, or industrial buildings where the cubic capacity affects rental rates or value. For example, a cold storage facility's value is often based on cubic feet of refrigerated space available for rent.
More Math & Stats Questions
What is the area of a triangular lot with a base of 120 feet and a height of 80 feet?
An irregular lot has the following measurements: Side A = 100', Side B = 150', Side C = 120', Side D = 180'. If the lot can be divided into two rectangles (100' × 150' and 120' × 30'), what is the total area?
A property has a potential gross income of $180,000, vacancy and collection loss of 7%, and operating expenses of $65,000. What is the NOI?
A property generates $120,000 in net operating income and is valued at $1,500,000. What is the capitalization rate?
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