A building measures 80 feet long, 60 feet wide, and 12 feet high. What is the volume in cubic feet?
Correct Answer
B) 57,600 cubic feet
Volume is calculated by multiplying length × width × height. 80 feet × 60 feet × 12 feet = 57,600 cubic feet.
Why This Is the Correct Answer
Option B is correct because volume is calculated using the formula: Volume = Length × Width × Height. Substituting the given measurements: 80 feet × 60 feet × 12 feet = 57,600 cubic feet. This straightforward multiplication gives us the total three-dimensional space contained within the building. The calculation follows the standard geometric principle for determining the volume of a rectangular prism or box-shaped structure.
Why the Other Options Are Wrong
Option A: 4,800 cubic feet
Option A (4,800 cubic feet) appears to be the result of multiplying only length × width (80 × 60 = 4,800), which gives square footage rather than cubic footage. This represents a two-dimensional calculation missing the height component.
Option C: 152 cubic feet
Option C (152 cubic feet) is far too small and appears to be the result of adding the dimensions (80 + 60 + 12 = 152) rather than multiplying them. This fundamental error confuses addition with the multiplication required for volume calculations.
Option D: 9,600 cubic feet
Option D (9,600 cubic feet) could result from multiplying 80 × 12 × 10 or similar miscalculation, possibly from misreading one of the dimensions or making an arithmetic error in the multiplication process.
LWH Volume Box
Remember 'LWH' - Length × Width × Height. Visualize stacking square floor plans (L×W) up to the ceiling height (H) to fill the entire box-shaped space.
How to use: When you see three building dimensions, immediately think 'LWH' and multiply all three numbers together. If you only see two dimensions, you're calculating area (square feet), not volume (cubic feet).
Exam Tip
Always check your units - cubic feet requires three dimensions multiplied together. If your answer seems too small, you may have forgotten to include the height dimension.
Common Mistakes to Avoid
- -Calculating area instead of volume by omitting height
- -Adding dimensions instead of multiplying them
- -Confusing square feet with cubic feet in the final answer
Concept Deep Dive
Analysis
This question tests fundamental geometric calculation skills essential for real estate appraisers who must accurately determine building volumes for various valuation purposes. Volume calculations are critical in cost approach valuations, particularly when estimating construction costs or determining cubic foot pricing for certain property types. The question requires understanding three-dimensional measurement and the mathematical relationship between length, width, and height. Appraisers frequently encounter volume calculations when dealing with warehouses, industrial buildings, or when cubic footage is a relevant unit of comparison.
Background Knowledge
Volume calculations require understanding that cubic measurements involve three dimensions multiplied together, unlike area calculations which only involve two dimensions. Real estate appraisers must distinguish between square footage (area) and cubic footage (volume) depending on the valuation method and property type being analyzed.
Real-World Application
Appraisers use volume calculations when valuing warehouses priced per cubic foot, determining storage capacity for industrial properties, or calculating construction costs for buildings where cubic footage is the relevant unit of measurement rather than square footage.
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?
A building has potential gross income of $180,000, vacancy and collection loss of 8%, and operating expenses of $54,000. What is the net operating income?
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