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An open cylinder of given surface will have maximum volume if radius =

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height

$\frac{1}{2}$ (height)

2 (height)

3 (height)

answer is A.

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Detailed Solution

$2 π r h + π r^{2} = k$

$\Rightarrow V = π r^{2} h = π r^{2} (\frac{k - π r^{2}}{2 π r}) = \frac{1}{2} (k r - π r^{3})$

$\Rightarrow f^{1} (r) = 0 \Rightarrow k = 3 π r^{2} h = \frac{3 {πr}^{2} - 2 {πr}^{2}}{2 πr} = r$

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