A warehouse measures 200 feet by 150 feet with a ceiling height of 24 feet. What is the total volume?
Correct Answer
B) 720,000 cubic feet
Volume is calculated as length × width × height. 200 × 150 × 24 = 720,000 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: 200 feet × 150 feet × 24 feet = 720,000 cubic feet. This calculation follows the standard geometric formula for rectangular prisms, which applies to most commercial buildings. The answer represents the total three-dimensional space within the warehouse that can be utilized for storage or other purposes.
Why the Other Options Are Wrong
Option A: 30,000 cubic feet
Option A (30,000 cubic feet) appears to be the result of multiplying length × width (200 × 150 = 30,000) but failing to include the height dimension, resulting in a square footage calculation rather than volume.
Option C: 374 cubic feet
Option C (374 cubic feet) is far too small and doesn't follow any logical calculation pattern from the given dimensions, suggesting a fundamental error in understanding the volume formula or arithmetic.
Option D: 7,200 cubic feet
Option D (7,200 cubic feet) appears to be the result of an incorrect calculation, possibly 200 × 24 × 1.5 or another mathematical error that doesn't properly incorporate all three dimensions.
LWH Volume Box
Remember 'LWH' - Length × Width × Height. Visualize stacking boxes: first you need the floor area (L×W), then multiply by how many layers high (H) you can stack them.
How to use: When you see a volume question, immediately write 'L × W × H =' and fill in the dimensions. Always check that your answer makes sense - a large warehouse should have hundreds of thousands of cubic feet.
Exam Tip
Always double-check your multiplication by estimating: 200 × 150 is about 30,000, then × 24 is about 720,000. This quick estimation can help you avoid calculation errors.
Common Mistakes to Avoid
- -Forgetting to multiply by height and only calculating square footage
- -Mixing up the order of operations or misplacing decimal points
- -Using the wrong units or converting between units incorrectly
Concept Deep Dive
Analysis
This question tests the fundamental geometric calculation of volume for three-dimensional spaces, which is essential in real estate appraisal for determining storage capacity, rental rates per cubic foot, and property valuations. Volume calculations are particularly important for commercial properties like warehouses where space utilization and storage capacity directly impact property value. The question requires understanding that volume is a three-dimensional measurement that incorporates length, width, and height. Appraisers must be proficient in these basic calculations as they form the foundation for more complex valuation methods and are frequently used in cost approach calculations.
Background Knowledge
Volume calculations are fundamental in real estate appraisal, particularly for commercial properties where cubic footage affects rental rates and property values. Appraisers must understand that volume equals length × width × height for rectangular spaces, and this measurement is crucial for determining storage capacity, HVAC requirements, and comparative analysis.
Real-World Application
Warehouse appraisers use volume calculations to determine storage capacity for lease rates, compare properties on a per-cubic-foot basis, and calculate construction costs. Industrial tenants often pay rent based on both square footage and ceiling height since higher ceilings allow for more storage.
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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