Which of the following is the total number of whole boxes that measure 2 ft * 2 ft * 2 ft that can be stored in a room that measures 9 ft * 9 ft * 9 ft, if the size of the boxes cannot not be altered?
125
64
18
91
Correct Answer : B
Number of boxes in the room is equal to the volume of the room divided by the volume of one box
Volume of the room=9 ft*9 ft*9 ft= 729 ft3
Volume of one box = 2 ft* 2 ft * 2 ft= 8 ft3
Number of boxes= 729 ft3/ 8 ft3= 91.125 boxes
Thus, the room can store 91.125 boxes, which is about 91 boxes.
However, the room’s dimensions are 9 ft x 9 ft x 9 ft, and the boxes are 2 ft x 2 ft x 2 ft. To determine how many boxes fit along each dimension:
- In the 9 ft length, you can fit \(\frac{9}{2} = 4.5\) boxes, which means only 4 whole boxes fit along this dimension.
- In the 9 ft width, you can fit 4 whole boxes.
- In the 9 ft height, you can fit 4 whole boxes.
Therefore, the total number of boxes that fit is:
\(4×4×4=64\ boxes\)
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