19. 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?
Answer: B
64 whole boxes can be stored in the room.
The total number of whole boxes that measure 2ft x 2ft x 2ft that can be stored in a 9ft x 9ft x 9ft room is 64. This is calculated by determining how many boxes can fit along each dimension of the room.
A) 18
Option A is incorrect as it underestimates the capacity of the room. Given the dimensions of the room, one can fit 4 boxes along each side (since 9/2 = 4.5, and only whole boxes can be counted), leading to a total of 4 x 4 x 4 = 64 boxes.
B) 64
Option B is correct. The calculation for the number of boxes is based on dividing the room dimensions by the box dimensions: 9ft ÷ 2ft = 4.5, meaning 4 whole boxes fit along each dimension. Thus, the total is 4 boxes per dimension multiplied together: 4 x 4 x 4 = 64 boxes.
C) 125
Option C is incorrect as it suggests that the room can hold more boxes than its dimensions allow. The calculation shows that the maximum number of boxes is limited to 64 based on the whole number fit along each dimension of the room.
D) 92
Option D is also incorrect. This number does not represent a whole number of boxes that can fit based on the room's dimensions and the size of the boxes. The correct calculation shows that only 64 boxes can be accommodated.
Conclusion
The correct answer is 64 whole boxes, as determined by the spatial constraints of the room and the size of the boxes. All other options either miscalculate the capacity or suggest an impossible arrangement within the given dimensions. Thus, Option B accurately reflects the maximum storage capacity in this scenario.