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Question Number 60422 by Tawa1 last updated on 20/May/19

Commented by MJS last updated on 20/May/19

$${\mathrm{what}}^{\prime }\mathrm{s}\mathrm{a}‘‘\mathrm{lidless}{\mathrm{box}}^{″}?$$$$\mathrm{what}\mathrm{are}\mathrm{the}‘‘{\mathrm{ends}}^{″}\mathrm{of}\mathrm{a}\mathrm{box}?$$

Commented by Tawa1 last updated on 20/May/19

$$\mathrm{I}{\mathrm{don}}^{\prime }\mathrm{t}\mathrm{know}\mathrm{sir}.\mathrm{that}\mathrm{is}\mathrm{the}\mathrm{question}.$$

Commented by Tawa1 last updated on 20/May/19

$$\mathrm{Maybe}\mathrm{question}\mathrm{is}\mathrm{wrong}\mathrm{sir}$$

Commented by MJS last updated on 20/May/19

$$\mathrm{if}{\mathrm{it}}^{\prime }\mathrm{s}\mathrm{a}\mathrm{box}\mathrm{with}\mathrm{square}\mathrm{sides}\mathrm{and}\mathrm{floor}\mathrm{but}$$$$\mathrm{without}\mathrm{a}\mathrm{cap}\mathrm{the}\mathrm{volume}\mathrm{is}{a}^3=3.5\mathrm{and}\mathrm{the}$$$$\mathrm{surface}\mathrm{is}5a^2$$$$5{\left(\sqrt[3]{3.5}\right)}^2\approx 11.53$$

Commented by Tawa1 last updated on 20/May/19

$$\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}$$

Answered by mr W last updated on 21/May/19

$$boxwithoutlid$$$$boxwithsquarebaseb\times b$$$$heightofboxh$$$$V=b^{2}h$$$$\Rightarrow h=\frac{V}{b^2}$$$$S=b^2+4bh=b^2+\frac{4V}{b}$$$$\frac{dS}{db}=2b-\frac{4V}{b^2}=0$$$$\Rightarrow b=\sqrt[3]{2V}=\sqrt[3]{2\times 3.5}=\sqrt[3]{7}=1.913m$$$$S_{min}=1.{913}^2+\frac{4\times 3.5}{1.913}=10.978m^2$$

Commented by Tawa1 last updated on 21/May/19

$$\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}$$

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