You’ve got a 10 x 10 x 10 cube made up of 1 x 1 x 1 smaller cubes. The outside of the larger cube is completely painted red. On how many of the smaller cubes is there any red paint?
Answer:
Solution 1: First, note that the larger cube is made up of 1000 smaller cubes. The easiest way to think about this is how many cubes are NOT painted?
8 x 8 x 8 inner cubes are not painted which equals 512 cubes. Therefore, 1000 – 512 = 488 cubes that have some paint.
Solution 2: We can calculate this by saying that two 10 x 10 sides are painted (2*10*10 = 200) plus two 10 x 8 sides (2*10*8 = 160) plus two 8 x 8 sides (2*8*8 = 128).
200 + 160 + 128 = 488 cubes.
Solution 1: First, note that the larger cube is made up of 1000 smaller cubes. The easiest way to think about this is how many cubes are NOT painted?
8 x 8 x 8 inner cubes are not painted which equals 512 cubes. Therefore, 1000 – 512 = 488 cubes that have some paint.
Solution 2: We can calculate this by saying that two 10 x 10 sides are painted (2*10*10 = 200) plus two 10 x 8 sides (2*10*8 = 160) plus two 8 x 8 sides (2*8*8 = 128).
200 + 160 + 128 = 488 cubes.
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