I still don't get this. We know that 1728 is the total volume of the bigger cube and the smaller cube has volume of 8 then shouldn't the answer be 216? How does one jump from

Cubes of 2x2x2 in a 12x12x12 cube= 6x6x6

We have 6 cubes so:

Total of cubes= 6^4=1296.

1728/8 = 216
So, we can cut 216 small (2 x 2 x 2) blocks from ONE large (12 x 12 x 12) block

The question asked us to find how many small blocks we can cut from SIX large blocks.
So, we need to take your answer (216) and multiply it by SIX to get 1296




By dividing 12x12x12 (the volume of ONE large block) by 2x2x2 (the volume of 1 small block), @jpalaciosm determined that we can cut 6x6x6 (aka 216) small blocks from one large block.
So to find the number of small blocks we can cut from SIX large blocks, we must take 6x6x6 and multiply it by 6 to get 6x6x6x6

Does that help?

Thanks Brent! Helped immensely!

What is the maximum number of 2-inch by 2-inch by 2-inch solid cubes that can be cut from six solid cubes that are 1 foot on each side? (12 inches = 1 foot)

Volume of small solid cubes = 2*2*2=8
Volume of 1 Big Cube = 12*12*12=1728
if you cut 1 cube you get 1728/8 = 216
You have to cut 6 so, 216*6=1296 option D

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