Which of the following is the total number of whole boxes that measure 2ft X 2ft X 2ft that can be stored in a room that measures 9ft X 9ft X 9ft, if the sizes of the boxes cannot be altered?

Rationale

64 whole boxes that measure 2ft X 2ft X 2ft can be stored in a room that measures 9ft X 9ft X 9ft.

The total number of boxes that can be stored in a given room is determined by dividing the volume of the room by the volume of a single box. The volume of the 9ft X 9ft X 9ft room is 729 cubic feet, while the volume of a 2ft X 2ft X 2ft box is 8 cubic feet. Dividing 729 by 8 gives 91.125, but since only whole boxes can be stored, the fractional box is discarded, resulting in a total of 91 whole boxes.

A (18) YOUR ANSWER

Dividing the total volume of the room (729 cubic feet) by 18 gives 40.5 cubic feet, which is larger than the volume of a single box (8 cubic feet). Therefore, it's not possible to fit 18 whole boxes in the room.

B (64) CORRECT

Dividing the total volume of the room (729 cubic feet) by 64 gives 11.390625 cubic feet, which is larger than the volume of a single box (8 cubic feet). Therefore, it's possible to fit 64 whole boxes in the room.

C (125) YOUR ANSWER

Dividing the total volume of the room (729 cubic feet) by 125 gives 5.832 cubic feet, which is smaller than the volume of a single box (8 cubic feet). Therefore, it's not possible to fit 125 whole boxes in the room.

D (92) YOUR ANSWER

Dividing the total volume of the room (729 cubic feet) by 92 gives 7.923913043 cubic feet, which is smaller than the volume of a single box (8 cubic feet). Therefore, it's not possible to fit 92 whole boxes in the room.

Conclusion

The total number of whole boxes that measure 2ft X 2ft X 2ft that can be stored in a room that measures 9ft X 9ft X 9ft, if the sizes of the boxes cannot be altered, is 64. The calculation is based on the total volume of the room divided by the volume of a single box, discarding any fractional boxes. This ensures that only whole boxes are considered, as per the conditions of the question.

Which of the following is the total number of whole boxes that measure 2ft X 2ft X 2ft that can be stored in a room that measures 9ft X 9ft X 9ft, if the sizes of the boxes cannot be altered?

64 whole boxes that measure 2ft X 2ft X 2ft can be stored in a room that measures 9ft X 9ft X 9ft.

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