A rectangular room is 16 feet long, 12 feet wide, and 9 feet high. If the room is divided into two equal parts by a wall parallel to the width, what is the volume of each smaller room?
- 864 cubic feet (correct answer)
- 1,152 cubic feet
- 1,296 cubic feet
- 1,728 cubic feet
- 2,304 cubic feet
Explanation: When you encounter volume problems involving room divisions, remember that volume equals length × width × height, and you need to determine how the division affects these dimensions. The original room has dimensions 16 feet long, 12 feet wide, and 9 feet high, giving it a total volume of cubic feet. The key insight is understanding what "divided by a wall parallel to the width" means. Since the wall is parallel to the width (12 feet), it runs across the length dimension, splitting the 16-foot length into two 8-foot sections. Each smaller room now measures 8 feet long, 12 feet wide, and 9 feet high. The volume of each smaller room is cubic feet, confirming that A is correct. Looking at the wrong answers: B (1,152) might result from incorrectly dividing the width instead of length, creating rooms that are 16 × 6 × 9. C (1,296) could come from mistakenly dividing the height, yielding 16 × 12 × 4.5, then rounding errors. D (1,728) is the original room's total volume—a trap for students who forget to account for the division entirely. Remember this pattern: when a room is divided by a wall "parallel to" a dimension, that wall runs along that dimension but splits the perpendicular dimension in half. Always identify which measurement gets divided, then calculate the new volume using the modified dimensions.