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Question Number 61322 by Tawa1 last updated on 31/May/19

Answered by MJS last updated on 02/Jun/19

$$\mathrm{the}\mathrm{cuboid}\mathrm{with}\mathrm{the}\mathrm{greatest}\mathrm{volume}\mathrm{at}\mathrm{a}$$$$\mathrm{given}\mathrm{surface}\mathrm{is}\mathrm{a}\mathrm{cube}$$$$$$$$S\mathrm{urface}=2a^2+4ab=216\Rightarrow b=\frac{54}{a}-\frac{a}{2}$$$$V\mathrm{olume}=a^{2}b=54a-\frac{1}{2}{a}^3$$$$V^{\prime }=54-\frac{3}{2}{a}^2=0\Rightarrow a=6\Rightarrow b=6$$

Commented by Tawa1 last updated on 02/Jun/19

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

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