Fitting cubes and cuboids.

Adeline Leng
Adeline Leng used Ask the Experts™
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What is the maximum number of 5 cm cubes that can fit into a rectangular box measuring 28cm by 42 cm by 36 cm?
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Database and Application Developer
Commented:
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.
Mike EghtebasDatabase and Application Developer

Commented:
The solution provided is the correct answer.

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