A) \[\sqrt{7}:1\]
B) \[\sqrt{7}:2\]
C) \[\sqrt{7}:3\]
D) \[\sqrt{7}:4\]
Correct Answer: B
Solution :
[b] \[x\times 2x\times 4x={{y}^{3}}\] or \[8{{x}^{3}}={{y}^{3}}\] or \[y=2x\] \[\therefore \,\,\,\,\,\,\frac{Diagonal\text{ }of\text{ }cuboid}{Diagonal\text{ }of\text{ }cube}\] \[=\frac{\sqrt{{{(4x)}^{2}}+{{(2x)}^{2}}+{{x}^{2}}}}{y\sqrt{3}}=\frac{\sqrt{21{{x}^{2}}}}{y\sqrt{3}}=\frac{\sqrt{7}}{2}\]
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