A) 4
B) \[\frac{1}{\sqrt{2}}\]
C) 2
D) \[\frac{1}{2}\]
Correct Answer: B
Solution :
Let radius and height of original cylinder be \[{{r}_{1}}\]and \[{{h}_{1}}\]respectively \[\therefore \]Volume of original cylinder \[=\pi r_{1}^{2}{{h}_{1}}\] Also, let radius of new cylinder be \[{{r}_{2}}\] and height of new cylinder \[=2\times \](height of original cylinder) \[=2\times {{h}_{1}}=2{{h}_{1}}\] \[\therefore \]Volume of new cylinder \[=\pi r_{2}^{2}.2{{h}_{1}}\] According to question, Volume of original cylinder = Volume of new cylinder \[\Rightarrow \]\[\pi r_{1}^{2}{{h}_{1}}=\pi r_{2}^{2}.2{{h}_{1}}\Rightarrow r_{1}^{2}=2r_{2}^{2}\Rightarrow {{r}_{2}}=\frac{1}{\sqrt{2}}{{r}_{1}}\] Hence, radius of base of new cylinder must be multiplied by \[\frac{1}{\sqrt{2}}\]so that the new cylinder has same volume as original.
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