SOLUTION: Sorry but I do not know how to change topic. A closed cardboard box measuring 7cm by 14cm by 5cm is filled with unit cubes ( 1cm by 1cm by 1cm). How many of these unit cubes touc

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Question 1001500: Sorry but I do not know how to change topic.
A closed cardboard box measuring 7cm by 14cm by 5cm is filled with unit cubes ( 1cm by 1cm by 1cm). How many of these unit cubes touch the box with at least one face? Thank you
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
The box contains 7%2A14%2A5=490 unit cubes forming a 7cm by 14cm by 5cm prism.
If you remove the cubes that are touching the box walls, you are removing
the top 1-cm layer and the bottom 1-cm layer of that prism,
the front 1-cm layer and the back 1-cm layer, and
the leftmost 1-cm layer and the rightmost 1-cm layer,
and you are left with a prism measuring
7cm-1cm-1cm=5cm by
14cm-1cm-1cm=12cm by
5cm-1cm-1cm=3cm .
That prism will be made of 5%2A12%2A3=180 unit cubes.
The unit cubes that touched the box with at least one face are the unit cubes removed:
490-180=highlight%28310%29 .