A Cube Is Made Of White Material, But The Exterior Is Painted Black. If The Cube Is Cut Into 125 Smaller Cubes Of Exactly The Same Size, How Many Of The Cubes Will Have 2 Of Their Sides Painted Black?
Answer:
125 = 53, so the larger cube is divided into cubes having 1/5 the edge dimension of the original. Each lip of the divided cube will have 2 corner cubes (with 3 sides painted) and 3 edge cubes (with 2 sides painted).
A cube has 12 edges. 3 cubes on respectively edge have 2 sides painted, so there are 36 smaller cubes that enjoy 2 sides painted.
8 have 3 sides painted
36 have 2 sides painted
54 have 1 side painted
27 enjoy no sides painted
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