Fitting cubes and cuboids.

What is the maximum number of 5 cm cubes that can fit into a rectangular box measuring 28cm by 42 cm by 36 cm?
Adeline LengAsked:
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Mike EghtebasDatabase and Application DeveloperCommented:
First, we need to find out how many 5 cm block can fit in each dimension:

28cm / 5 cm = 5.6 --> 5     with 1 mm gaps
 42cm / 5 cm = 8.4 --> 8    with about 0.44 mm gaps
 36cm / 5 cm = 7.2 --> 7     with .25 mm gaps

Then, multiply them to get the result we need:

5*8*7 = 280 little 5 cm cubes

The gaps above are necessary for one to fit the small blocks in the big box. If necessary, fill the gaps with some wrapper or filler items.

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Mike EghtebasDatabase and Application DeveloperCommented:
The solution provided is the correct answer.
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