A warehouse building measures 100 feet long, 80 feet wide, and has a ceiling height of 20 feet. What is the cubic volume?
Correct Answer
B) 160,000 cubic feet
Volume is calculated by multiplying length × width × height: 100 feet × 80 feet × 20 feet = 160,000 cubic feet.
Why This Is the Correct Answer
Option B is correct because volume is calculated using the formula: Length × Width × Height. Substituting the given measurements: 100 feet × 80 feet × 20 feet = 160,000 cubic feet. This calculation properly accounts for all three dimensions of the warehouse space. The result represents the total enclosed air space within the building, which is crucial for determining storage capacity and mechanical system requirements.
Why the Other Options Are Wrong
Option A: 8,000 cubic feet
Option A (8,000 cubic feet) appears to be the result of multiplying only length × width (100 × 80 = 8,000), completely omitting the height dimension, which would give square footage rather than cubic volume.
Option C: 1,600 cubic feet
Option C (1,600 cubic feet) seems to result from an error in calculation, possibly confusing the dimensions or making an arithmetic mistake, as this number doesn't correspond to any logical combination of the given measurements.
Option D: 200 cubic feet
Option D (200 cubic feet) appears to be the sum of the three dimensions (100 + 80 + 20 = 200) rather than their product, which is a fundamental misunderstanding of how volume is calculated.
LWH Volume Pyramid
Remember 'LWH' (Length × Width × Height) by thinking 'Let's Work Hard' - and visualize stacking square floor areas (L×W) up to the ceiling height (H) to fill the entire cubic space.
How to use: When you see a volume question, immediately write 'L × W × H =' and identify each dimension from the problem before multiplying, ensuring you don't skip the height dimension.
Exam Tip
Always double-check that your answer is in cubic units (cubic feet, cubic yards) for volume questions, and verify you've used all three given dimensions in your calculation.
Common Mistakes to Avoid
- -Calculating area (L×W) instead of volume (L×W×H)
- -Adding dimensions instead of multiplying them
- -Confusing square footage with cubic footage in the final answer
Concept Deep Dive
Analysis
This question tests the fundamental geometric calculation of cubic volume, which is essential for real estate appraisers when determining storage capacity, heating/cooling requirements, and certain valuation methods. Volume calculations are particularly important for warehouse, industrial, and storage properties where three-dimensional space directly impacts utility and value. The concept requires understanding that volume is a three-dimensional measurement that accounts for length, width, and height simultaneously. This basic mathematical skill forms the foundation for more complex appraisal calculations involving building capacity and functional utility.
Background Knowledge
Volume calculation requires multiplying all three spatial dimensions: length, width, and height, expressed in cubic units. This differs from area calculations which only use two dimensions and are expressed in square units.
Real-World Application
Appraisers use cubic volume calculations to determine warehouse storage capacity for income approach valuations, calculate heating/cooling costs for operating expense analysis, and compare functional utility between similar industrial properties.
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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