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A 10cmx3 cube is cut in2 1cmx3 cubes are glued together to form the largest possible cube which looks solid from any point on the outside but is hollow inside What is the no of smaller cubes left over?
Wiki User
∙ 14y ago
The equation for the number of 1 cm3 cubes to form a n3 cm3 hollow cube (n>1):
6n2-12n+8 (hint: cubes have 6 faces, 12 edges, and 8 vertices)
I'm not sure whether you are asking about a 10 cm3 cube or a 103 cm3 cube.
Since you can't divide a 10 cm3 cube into 1 cm3 pieces, I am going to assume you mean a 103 cm3 cube. This cube will yield 1000 1 cm3 cubes.
For n=13, 6n2-12n+8 = 866
For n=14, 6n2-12n+8 = 1016
So, with 1000 little cubes, you can form a 13x13x13 cm hollow cube with 134 little cubes left out.
Wiki User
∙ 14y ago
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