343 smaller but identical cubes are placed together to form a big cube. What is the number of small cubes that get cut when the big cube is cut by one diagonal cut?
Answers
Answer:
The 343 cubes will form 7 layers of 7*7 = 49 cubes in each layer.
343^(1/3) = 7
A cube has 8 vertices, so 8 cubes have 3 faces painted.
A cube has 12 edges, so 12*(7–2) = 60 cubes have 2 faces painted.
A cube has 6 faces, so 6*(7–2)^2 = 150 cubes have 1 face painted.
The innermost (7–2)^3 = 125 cubes have no painted surface.
None of the 4 options is correct. Only 210 cubes have either 1 or 2 faces painted.
If cubes without any painted surface are also considered then the number is 125+210 = 335. (Choice d)
Thus the total = 8+60+150+125 = 343 cubes
Answer:
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Step-by-step explanation:
The 343 cubes will form 7 layers of 7*7 = 49 cubes in each layer.
343^(1/3) = 7
A cube has 8 vertices, so 8 cubes have 3 faces painted.
A cube has 12 edges, so 12*(7–2) = 60 cubes have 2 faces painted.
A cube has 6 faces, so 6*(7–2)^2 = 150 cubes have 1 face painted.
The innermost (7–2)^3 = 125 cubes have no painted surface.
None of the 4 options is correct. Only 210 cubes have either 1 or 2 faces painted.
If cubes without any painted surface are also considered then the number is 125+210 = 335.
Thus the total = 8+60+150+125 = 343 cubes.