Math CentralQuandaries & Queries


Question from Tom:

I have a box that has internal dimensions of: 24in. H x 14in. W x 14in. D.
How many cubic feet is this internal space?

We have two responses for yoy


The number of cubic inches is length x width x height. Now you need to convert that to cubic feet. One cubic foot measures 12 in x 12 in x 12 in. How many of those do you have?

Alternatively, convert the side measurements to feet first.

Good luck.



Think about a box with internal dimensions of 1 ft by 1 ft by 1 ft. Its volume is 1 cubic foot. Now suppose you want to fill it with block that are 1 in by 1 in by 1 in. You start by laying 12 of the blocks along one side of the bottom of the box. Then you can place another row of 12 blocks beside it and another row of 12 blocks beside the second row. Continue this with 12 rows of 12 blocks to cover the bottom of the box. 12 rows of 12 blocks each is 12 × 12 = 144 blocks.

Now start another layer in the same fashion on top of the first layer, and then another on top of the second layer and so on until you have 12 layers of 144 blocks each. Thus you have filled the box with 12 × 144 = 1728 blocks. Thus 1 cubic foot = 1728 cubic inches.

Your box is 24 in by 14 in by 14 inches so that's 24 × 14 × 14 = 4704 cubic inches which is 4704/1728 = 2.72 cubic feet.


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