A) \[\frac{{{x}^{2}}}{2\pi }\]
B) \[\frac{x}{2\sqrt{\pi }}\]
C) \[\frac{\sqrt{2x}}{\pi }\]
D) \[\frac{x}{2\sqrt{\pi }}\]
Correct Answer: B
Solution :
Let the height of cylinder and rectangular box be h. Volume of cylinder\[=\pi {{r}^{2}}h\] \[\therefore \]Volume of rectangular box\[=x\times x\times h={{x}^{2}}h\] According to question, Volume of cylinder \[=\frac{1}{4}\times \]Volume of rectangular box \[\Rightarrow \]\[\pi {{r}^{2}}h=\frac{1}{4}\times {{x}^{2}}h\Rightarrow {{r}^{2}}=\frac{{{x}^{2}}}{4\pi }\]or \[r=\frac{x}{2\sqrt{\pi }}\]
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