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:
Who is Participating?

[Product update] Infrastructure Analysis Tool is now available with Business Accounts.Learn More

x
I wear a lot of hats...

"The solutions and answers provided on Experts Exchange have been extremely helpful to me over the last few years. I wear a lot of hats - Developer, Database Administrator, Help Desk, etc., so I know a lot of things but not a lot about one thing. Experts Exchange gives me answers from people who do know a lot about one thing, in a easy to use platform." -Todd S.

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.
0

Experts Exchange Solution brought to you by

Your issues matter to us.

Facing a tech roadblock? Get the help and guidance you need from experienced professionals who care. Ask your question anytime, anywhere, with no hassle.

Start your 7-day free trial
Mike EghtebasDatabase and Application DeveloperCommented:
The solution provided is the correct answer.
0
It's more than this solution.Get answers and train to solve all your tech problems - anytime, anywhere.Try it for free Edge Out The Competitionfor your dream job with proven skills and certifications.Get started today Stand Outas the employee with proven skills.Start learning today for free Move Your Career Forwardwith certification training in the latest technologies.Start your trial today
Math / Science

From novice to tech pro — start learning today.