A warehouse building measures 100 feet by 150 feet with a ceiling height of 20 feet. What is the total cubic volume?
Correct Answer
C) 300,000 cubic feet
Volume is length × width × height. 100 × 150 × 20 = 300,000 cubic feet.
Why This Is the Correct Answer
Option C is correct because it properly applies the volume formula: length × width × height = 100 feet × 150 feet × 20 feet = 300,000 cubic feet. This calculation multiplies all three dimensions to determine the total interior space volume. The answer represents the complete cubic capacity of the warehouse building. This is the standard method for calculating volume in rectangular structures.
Why the Other Options Are Wrong
Option A: 270 cubic feet
Option A (270 cubic feet) appears to be a random calculation error, possibly confusing perimeter calculations or making arithmetic mistakes, as it doesn't follow any logical geometric formula for the given dimensions.
Option B: 15,000 cubic feet
Option B (15,000 cubic feet) incorrectly calculates volume by only using two dimensions (100 × 150 = 15,000), completely omitting the height component, which reduces a three-dimensional calculation to a two-dimensional area calculation.
Option D: 30,000 cubic feet
Option D (30,000 cubic feet) makes an error in the calculation sequence, possibly multiplying 100 × 150 × 2 instead of 20, or making another arithmetic mistake that results in a tenfold understatement of the actual volume.
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). Count: L-W-H, multiply all three!
How to use: When you see any volume question, immediately write 'L × W × H =' and fill in the three given dimensions. Always check that you're using three numbers, not just two.
Exam Tip
Always double-check that you've used all three dimensions in volume calculations - length, width, AND height. Write out the formula first, then substitute the numbers.
Common Mistakes to Avoid
- -Forgetting to include the height dimension and only calculating area
- -Mixing up the order of operations or making arithmetic errors
- -Confusing volume calculations with perimeter or area calculations
Concept Deep Dive
Analysis
This question tests the fundamental geometric calculation of cubic volume, which is essential for real estate appraisers when determining warehouse storage capacity, HVAC requirements, and certain valuation methods. Volume calculations are particularly important for industrial properties where cubic footage directly impacts utility and value. The question requires applying the basic formula for rectangular volume: length × width × height. Understanding this concept is crucial for appraisers who must accurately measure and calculate building dimensions for various appraisal purposes.
Background Knowledge
Volume calculations require understanding three-dimensional geometry where length, width, and height are multiplied together to determine cubic capacity. In real estate appraisal, cubic measurements are essential for industrial properties, storage facilities, and buildings where interior volume affects value and utility.
Real-World Application
Appraisers use cubic volume calculations when valuing warehouses for storage capacity, determining HVAC system requirements, calculating construction costs per cubic foot, and assessing industrial properties where volume directly impacts rental rates and property value.
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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