A warehouse measures 200 feet by 150 feet with a ceiling height of 24 feet. What is the volume in cubic feet?
Correct Answer
C) 720,000 cubic feet
Volume = Length × Width × Height. 200 × 150 × 24 = 720,000 cubic feet.
Why This Is the Correct Answer
Option C is correct because it properly applies the volume formula: Volume = Length × Width × Height. Multiplying 200 feet × 150 feet × 24 feet equals 720,000 cubic feet. This calculation accounts for all three dimensions of the warehouse space. The systematic multiplication (200 × 150 = 30,000, then 30,000 × 24 = 720,000) yields the accurate total volume.
Why the Other Options Are Wrong
Option A: 30,000 cubic feet
This represents only the floor area (200 × 150 = 30,000) without accounting for the height dimension, making it a two-dimensional calculation rather than the required three-dimensional volume.
Option B: 374 cubic feet
This number appears to be the result of adding the dimensions (200 + 150 + 24 = 374) rather than multiplying them, which is completely incorrect for volume calculations.
Option D: 7,200 cubic feet
This appears to be an error where someone calculated 200 × 24 × 1.5 instead of 200 × 24 × 150, possibly confusing 150 feet with 1.5 or making a decimal placement error.
LWH Box Method
Remember 'LWH' (Length × Width × Height) by thinking 'Let's Work Hard' - visualize stacking flat boxes (L×W) up to the ceiling (×H) to fill the entire space.
How to use: When you see a volume question, immediately write 'L × W × H =' and identify each dimension from the problem, then multiply systematically: first L×W for area, then multiply by H for volume.
Exam Tip
Always double-check your multiplication by breaking large calculations into steps (200×150=30,000, then 30,000×24=720,000) and verify you're using all three dimensions given in the problem.
Common Mistakes to Avoid
- -Calculating only floor area (L×W) and forgetting height
- -Adding dimensions instead of multiplying them
- -Making arithmetic errors with large numbers
- -Confusing linear feet with cubic feet in the final answer
Concept Deep Dive
Analysis
This question tests the fundamental geometric calculation of volume for rectangular structures, 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 industrial properties like warehouses where three-dimensional space utilization directly impacts value. The question requires applying the basic volume formula for rectangular prisms and performing accurate multiplication with larger numbers. Understanding volume calculations is crucial for appraisers when comparing properties, determining functional utility, and calculating replacement costs for industrial buildings.
Background Knowledge
Volume calculations require understanding that volume measures three-dimensional space using the formula Length × Width × Height for rectangular structures. In real estate appraisal, volume is particularly important for industrial properties, storage facilities, and any space where cubic capacity affects value or utility.
Real-World Application
Appraisers use volume calculations when valuing warehouses for lease rates per cubic foot, determining storage capacity for logistics facilities, calculating replacement costs for industrial buildings, and comparing functional utility between similar 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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