A warehouse has interior dimensions of 120 feet × 80 feet × 20 feet high. What is the volume in cubic feet?
Correct Answer
B) 192,000 cubic feet
Volume = length × width × height = 120 × 80 × 20 = 192,000 cubic feet.
Why This Is the Correct Answer
Option B is correct because volume is calculated by multiplying length × width × height. Using the given dimensions: 120 feet × 80 feet × 20 feet = 192,000 cubic feet. This straightforward multiplication gives us the total interior volume of the warehouse space. The calculation follows the standard geometric formula for finding the volume of a rectangular prism, which is the shape of most warehouse interiors.
Why the Other Options Are Wrong
Option A: 9,600 cubic feet
Option A (9,600) appears to be the result of multiplying only length × width (120 × 80 = 9,600), which gives square footage rather than cubic footage. This is a common error where the height dimension is omitted from the calculation.
Option C: 220 cubic feet
Option C (220) appears to be the result of adding the three dimensions (120 + 80 + 20 = 220) rather than multiplying them. This fundamental mathematical error confuses addition with the multiplication required for volume calculations.
Option D: 19,200 cubic feet
Option D (19,200) could result from various calculation errors, such as dividing one of the dimensions by 10 or making an order of magnitude error during multiplication. This represents a significant miscalculation of the volume formula.
LWH Box Method
Remember 'LWH' - Length × Width × Height. Visualize stacking unit cubes to fill a box: you need cubes going across (length), back (width), and up (height). Think 'Love Will Help' to remember the order doesn't matter in multiplication.
How to use: When you see interior dimensions with three measurements, immediately think 'LWH' and multiply all three numbers together. Always check that your answer is in cubic units (cubic feet, cubic yards, etc.) for volume questions.
Exam Tip
Double-check your multiplication by breaking it into steps: first multiply two dimensions, then multiply that result by the third dimension. This reduces calculation errors and makes verification easier.
Common Mistakes to Avoid
- -Forgetting to include the height dimension and calculating area instead of volume
- -Adding dimensions instead of multiplying them
- -Making arithmetic errors during multiplication of large numbers
Concept Deep Dive
Analysis
This question tests fundamental geometric calculation skills essential for real estate appraisal, specifically the ability to calculate volume using the basic formula for rectangular prisms. Volume calculations are critical in commercial real estate appraisal for determining storage capacity, rental rates per cubic foot, and comparing properties based on usable space. The question requires multiplying three dimensions (length, width, and height) to determine total cubic footage. Understanding volume calculations is foundational for more complex appraisal concepts like cost approach calculations and highest and best use analysis.
Background Knowledge
Volume calculations require understanding that volume equals length × width × height for rectangular spaces, measured in cubic units. In real estate, volume is particularly important for warehouses, storage facilities, and industrial properties where three-dimensional space utilization affects value and rental rates.
Real-World Application
Appraisers use volume calculations when valuing warehouses for lease rates per cubic foot, determining storage capacity for logistics facilities, or calculating construction costs for industrial buildings where interior volume affects heating, cooling, and operational expenses.
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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