A) \[\sqrt{n}k\]
B) \[\frac{k}{\sqrt[3]{n}}\]
C) \[\sqrt[3]{n}k\]
D) \[\frac{\sqrt[3]{n}}{k}\]
Correct Answer: B
Solution :
Edge of big cube = k units Let the edge of small cube be ?a? units. \[\Rightarrow \]Volume of each small cube \[={{a}^{3}}\,cu.units;\] \[\Rightarrow \]Volume of big cube \[={{k}^{3}}\] Given there are ?n? small cubes \[\Rightarrow \]\[{{k}^{3}}=n.{{a}^{3}}\Rightarrow {{a}^{3}}=\frac{{{k}^{3}}}{n}\Rightarrow a=\frac{h}{\sqrt[3]{n}}\] \[\therefore \]Length of the edge of the new cube is \[\frac{k}{\sqrt[3]{n}}\]
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