A) 4 : 1
B) 4 : 3
C) 1 : 4
D) 2 : 3
Correct Answer: A
Solution :
Number of small cubes \[=\frac{\text{Volume}\,\,\text{of}\,\,\text{large}\,\,\text{cube}}{\text{Volume}\,\,\text{of}\,\,\text{a}\,\,\text{small}\,\,\text{cube}}\text{=}\frac{{{(4)}^{3}}}{{{1}^{3}}}=64\] Total surface area of the large cube\[=6{{(4)}^{2}}=96\,\,\text{c}{{\text{m}}^{2}}\] Total surface area of 1 small cube \[=6{{(1)}^{2}}=6\,\text{c}{{\text{m}}^{2}}\] Total surface area of 64 small cubes \[=64\times 6=384\,\,\text{c}{{\text{m}}^{2}}\] \[\therefore \] Required ratio = 384 : 96 or 4 : 1
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