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A storage pod was rented to hold merchandise for a sporting event. the boxes of merchandise are 1 cubic foot each. The volume of the inside of the storage pod is 1280 cubic feet. What are some possible dimensions, in feet, of the storage pod being used?

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Blitztiger
There are a large number of possibilities, since each box is 1 cubic foot. We do not know the exact dimensions of each box (could be 1 ft x 1 ft x 1 ft, or 2 ft x 0.5 ft x 1 ft, or 4 ft x 0.5 ft x 0.5 ft). But in the simplest case, where each box is 1 ft x 1 ft x 1 ft, some possible dimensions are:
10 ft x 16 ft x 8 ft
20 ft x 8 ft x 8 ft
5 ft x 16 ft x 16 ft
10 ft x 32 ft x 4 ft
And so on, as long as each of the storage box dimensions are divisible by the dimensions of the boxes (in this case, 1 ft)
frika

Since [tex] 1280=2^8\cdot 5 [/tex], the dimensions (only integer) that gives the volume of the storage pod 1280 cubic feet are:

1 ft·1 ft· 1280 ft,

1 ft·2 ft· 640 ft,

1 ft·4 ft· 320 ft,

1 ft·8 ft· 160 ft,

1 ft·16 ft· 80 ft,

1 ft·32 ft· 40 ft,

1 ft·64 ft· 20 ft,

1 ft·128 ft· 10 ft,

1 ft·256 ft· 5 ft,

2 ft·2 ft· 320 ft,

2 ft·4 ft· 160 ft,

2 ft·8 ft· 80 ft,

2 ft·16 ft· 40 ft,

2 ft·32 ft· 20 ft,

2 ft·64 ft· 10 ft,

2 ft·128 ft· 5 ft,

4 ft·4 ft· 80 ft,

4 ft·8 ft· 40 ft,

4 ft·16 ft· 20 ft,

4 ft·32 ft· 10 ft,

4 ft·64 ft· 5 ft,

5 ft·8 ft ·32 ft,

5 ft·16 ft ·16 ft,

8 ft·8 ft ·20 ft,

8 ft·16 ft ·10 ft.

You can put the boxes of merchandise of volume 1 cubic foot each. If solve this question in integer numbers, then the dimensions of the box is 1 ft·1 ft· 1 ft and you can fit 1280 boxes in each storage pod listed above. If solve this question not only in integers, then there are a great amount of possible dimensions of a storage pod and boxes (for example, storage box has dimensions 0.5 ft· 2 ft· 1280 ft and boxes have dimensions 0.5 ft·2 ft· 1 ft and so on).

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