Bobo bought a 1 ft squared block of cheese. He needs to cut it into 3 in. cubes. The block is yellow outside but green on the inside. How many 3 in. cubes does it have? How many of the cubes have no yellow face, one yellow face, 2 yellow face, etc.

Question

Bobo bought a 1 ft squared block of cheese. He needs to cut it into 3 in. cubes. The block is yellow outside but green on the inside. How many 3 in. cubes does it have? How many of the cubes have no yellow face, one yellow face, 2 yellow face, etc.

Please help!!!

Answer 1

assuming you mean a 1 ft cube, then it has 4^3 = 64 smaller cubes.

The 8 corners have 3 faces yellow
The 12 edges have 2 blocks each with 2 faces yellow, making 24
The 6 faces have a 2x2=4 set of cubes with 1 face yellow, or 24
That leaves the interior 2x2x2=8 cubes all green