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Question Number 98278 by liki last updated on 12/Jun/20

Answered by mr W last updated on 12/Jun/20

$$sidelengthofsquare=a$$$$heightofbox=h$$$$volumeV=a^{2}h$$$$surfaceS=a^2+4ah=a^2+4a\frac{V}{a^2}=a^2+\frac{4V}{a}$$$$\frac{dS}{da}=2a-\frac{4V}{a^2}=0$$$$\Rightarrow a^3=2V$$$$\Rightarrow a=\sqrt[3]{2V}$$$$h=\frac{V}{a^2}=\frac{V}{\sqrt[3]{4V^2}}=\frac{\sqrt[3]{V}}{\sqrt[3]{4}}$$$$\Rightarrow \frac{h}{a}=\frac{1}{\sqrt[3]{4}\times \sqrt[3]{2}}=\frac{1}{2}$$

Commented by liki last updated on 12/Jun/20

$$..\mathbf{blessed}\mathbf{sir},\mathrm{i}\mathbf{appriciate}\mathbf{your}\mathbf{time}$$

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