Math CentralQuandaries & Queries


Question from Ashutosh, a student:

A rectangular block measuring 10 units by 8 units by 6 units is made up of cubes measuring 1 unit on a side. The base of the block is 10 units by 8 units. The outside of the block other than the base is painted red. How many of the unit cubes have exactly one face painted red?

We have two responses for you


I am going to look at a block measuring 4 units by 3 units by 3 units with base 3 units by 3 units. Again paint the outside other than the base red. How many of the unit cubes have exactly one face painted red?


I then looked for unit blocks that had exactly two faces painted red and over painted thee faces orange.


Finally I looked for unit cubes that had exactly three faces painted red and I over painted these faces green.


So I get

13 unit blocks with red paint on them,
16 unit blocks with orange paint on them,
4 unit blocks with green paint on them, and
3 unit blocks with no paint on them.

For a total of 3 × 3 × 4 = 36 blocks.

Can you do something similar foe your block?




Count the number of blocks on the exposed faces that aren't on a side or top edge.



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