A) \[12\,\,cm\]
B) \[6\,\,cm\]
C) \[18\,\,cm\]
D) \[3\,\,cm\]
Correct Answer: D
Solution :
Let the edges of the block are\[\frac{a}{r},\,\,a\]and\[ar\]. Then, \[\frac{a}{r}\cdot a\cdot ar=216\] \[\Rightarrow \] \[{{a}^{3}}=216\] \[\Rightarrow \] \[a=6\] and \[2\left[ \frac{a}{r}\cdot a+a\cdot ar+ar\cdot \frac{a}{r} \right]=252\] \[\Rightarrow \] \[2{{a}^{2}}\left[ \frac{1}{r}+r+1 \right]=252\] \[\Rightarrow \] \[\frac{1}{r}+r+1=\frac{252}{2\times 6\times 6}=\frac{7}{2}\] \[r+\frac{1}{r}=\frac{5}{2}\] \[\Rightarrow \] \[r=2\] Thus, shortest edge\[=\frac{a}{r}=\frac{6}{2}=3\,\,cm\]
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