A few days ago
Manda

one last question…for any math whizzes out there. thanks for helping!?

i got the information: “Picture a wire grid of cubes, 6 cubes on an edge. How many different cubes of all sizes are in this 6 by 6 by 6 grid of cubes? Count all the 1 by 1 by 1 cubes, all the 2 by 2 by 2 cubes, and so on. Don’t forget to count the entire 6 by 6 by 6 cube. Look to patterns for help.” this is kind of similar to my previous question….but this one i didn’t even know how to do and i really need to go to sleep soon and i still need to study so help would be much appreciated! thanks!!!

Top 2 Answers
A few days ago
TitoBob

Favorite Answer

If you draw a sketch of this mega-cube, and then start to look at the 1×1, 2×2, 3×3, etc. squares along one face, you will see that a pattern develops. There have to be 6x6x6=216 cubes 1×1. Then there will be 5x5x5=125 cubes 2×2, and so on. You can take it from there. The total is 441 in all.
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A few days ago
TurtleFromQuebec
1x1x1 cubes: 6^3 = 216

2x2x2 cubes: 5^3 = 125 (after all, there are 5 each way)

3x3x3 cubes: 4^3 = 64

etc etc.

Total 216+125+64+27+8+1 = 441 = 21^2 (by a famous formula)

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