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Help with this question please
- Thread starter bubby
- Start date
bubby said:megan has 1200 sugar cubes. what is the largest cube she could build with the sugar cubes? We have tried working backwards with the area of a cube equation but did not work.
When you build a large cube using the sugar cubes you have to work with, the large cube will have to be filled up with the small sugar cubes, right?
For example, if you build a cube that is THREE sugar cubes long, THREE sugar cubes wide, and THREE sugar cubes high, it will take 9 sugar cubes for the bottom, 9 sugar cubes for the middle layer, and 9 sugar cubes for the top layer. This is a total of 9 + 9 + 9 sugar cubes, or 27 sugar cubes. Note that 27 is 3 * 3 * 3.
If you build a big cube that is 4 sugar cubes long, 4 sugar cubes wide, and 4 sugar cubes high, it will take 16 sugar cubes for the bottom, 16 sugar cubes for the second layer, 16 sugar cubes for the third layer, and 16 sugar cubes for the top layer. That's 16 + 16 + 16 + 16, or 64 sugar cubes. Note that 4 * 4 * 4 is 64.
I think you need to work with the VOLUME of the big cube, rather than the area. For a cube,
volume = length * width * height............and in a cube, the length, width and height are the same
You can make a big cube whose volume is AT MOST 1200 if you have 1200 small sugar cubes to work with.
3*3*3 is 9
4*4*4 is 64
5*5*5 is 125
Does this give you an idea of how you can find the dimensions of the largest cube you could make with 1200 small sugar cubes? (You won't use them all up.....)