A warehouse is 80 feet wide, 120 feet long, and has ceilings 14 feet high. If 1,200 square feet of floor space is partitioned off for an office from floor to ceiling, how many cubic feet of space remain in the warehouse?

A warehouse is 80 feet wide, 120 feet long, and has ceilings 14 feet high. If 1,200 square feet of floor space is partitioned off for an office from floor to ceiling, how many cubic feet of space remain in the warehouse?

• A. 117,600
• B. 120,000
• C. 128,000
• D. 112,000

Answer: (A)

Removing a portion that runs from floor to ceiling means subtracting its volume from the total. The warehouse's total volume is width × length × height = 80 × 120 × 14 = 134,400 cubic feet. The carved-off office occupies floor area 1,200 square feet across the full height, so its volume is 1,200 × 14 = 16,800 cubic feet. Remaining space = 134,400 − 16,800 = 117,600 cubic feet.

Removing a portion that runs from floor to ceiling means subtracting its volume from the total.

The warehouse's total volume is width × length × height = 80 × 120 × 14 = 134,400 cubic feet.

The carved-off office occupies floor area 1,200 square feet across the full height, so its volume is 1,200 × 14 = 16,800 cubic feet.

Remaining space = 134,400 − 16,800 = 117,600 cubic feet.