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The Painted Cube - Maths Investigations
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- Words:
- 1112
- Submitted:
- Thu Jul 11 2002
... The Painted Cube. D.K A cube is painted on all its faces. It is then cut into 27 identical cubes. How many cubes have paint on. (a) 3 faces. (b) 2 faces. (c) 1 face. (d) 0 faces. A similar cube is painted on all six faces it is then cut into 64 identical cubes. How many cubes have paint on. (a) 3 faces. (b) 2 faces. (c) 1 face. (d) 0 faces. A cube made of 27 smaller ones has a length, width and height of 3. I know this because 3*3*3= 27. 3*3*3 3 Faces. = 8 2 Faces. = 12 1 Faces. = 6 0 Faces. = 1 Total. = 27 Already just by looking at the first cube I have realised that all the cubes will have 8 small cubes with three faces covered, noticed this as all cubes no matter what size always have 8 corners. A cube split into 64 identical cubes has lengths widths and heights of 4*4*4. 3 Faces. = 8 2 Faces. = 24 1 Faces. = 24 0 Faces. = 8 Total. = 64 My 4*4*4 cube has proven that all the
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