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A big cube is formed by rearranging the 160 coloured and 56 non-coloured similar cubes in such a way that the expouser of the coloured cubes to the outside is minimum. The percentage of exposed area that is coloured is:

a) 25.9%
b) 44.44%
c) 35%
d) 32%

Answer: b
Explanation: Total number of cubes = 160 + 56 = 216
Side of cube = 6 unit
No. of cubes without exposure = (6 – 2)3 = 64
Thus 64 cubes will be inside of a big cube
Now, rest cubes = 160 – 64 = 96
No. of cubes with one face outside = 6 × (4 × 4) = 96
Required % = $$\frac{{90 \times 100}}{{216}} = 44.44\% $$

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