): 216 small but identical cubes have been put together to form a large cube. This larger cube is now painted in all 6 faces.
21. How many of the smaller cubes have no faces painted at all.
a. 125 b. 27 c.64 d. 49
22. How many of the smaller cubes have exactly one face painted.
a. 96 b. 16 c.120 d. 112
23. How many of the smaller cubes have exactly two faces painted.
a. 56 b. 60 c. 64 d. 48
24. How many of the smaller cubes have exactly three faces painted.
a. 16 b. 8 c. 9 d. 27
25. How many more such small cubes will be required to cover this large cube completely.
a. 296 b. 212 c. 218 d. 224
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21. The smaller cubes have no faces painted=(n-2)^3=(6-2)^3=64
Therefore, option c is correct.
22. The smaller cubes have exactly one face painted= 6*(n-2)^2=6*(6-2)^2=96
Therefore, option a is correct.
23. The smaller cubes have exactly two faces painted= 12*(n-2)=12*(6-2)=48
Therefore, option d is correct.
24. The smaller cubes have exactly three faces painted means cubes on corners=8
Therefore, option b is correct.
25. The more smaller cubes needed to cover this large cube=8^3-6^3=512-216=296
Therefore, option a is correct.
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