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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

Ashutosh,

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?

red

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

orange

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

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?

Penny

 

Ashutosh,

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

Stephen.

 

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