Question 172609: Ten solid cubes ech measuring 4 inches on a side, are to be packed into a rectangular carton. Which of the following dimensions of a carton hold these 10 cubes with the least amount of wasted space?
Answer by colliefan(242)   (Show Source):
You can put this solution on YOUR website! Ten solid cubes ech measuring 4 inches on a side, are to be packed into a rectangular carton. Which of the following dimensions of a carton hold these 10 cubes with the least amount of wasted space?
I don't know what your 4 options are. Draw a diagram of rectangular carton and figure out the volumes of the rectangular air spaces left when the cubes are in place. A box with dimensions that are multiples of 4 will likely be the best solution.
For example, a box that was 8" long x 8" wide x 12" tall would have 4 cubes packed in solidly on the bottom 2 levels, but only 2 cubes on the top level. The empty space would be a 4" wide x 8" long x 4" high and so have a volume of 128 cu in.
A different box that was 8" x 10" x 12" would have empty space not only at the top level where the 2 missing cubes are, but would have a space at one end of the box that was 8" x 2" x 12". The wasted space in this box would be 128 cu in from the missing 1 cubes plus 192 cu in at the end of the box.
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