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Problem 560

Which 3 -dimensional rectangular box of a given volume \(\mathrm{V}\) has the least surface area?

Expert verified

To minimize the surface area of a 3-dimensional rectangular box with a given volume \(V\), the dimensions should be:
Length (l): \(\sqrt{\dfrac{2V}{\sqrt[3]{2V}}}\)
Width (w): \(\sqrt[3]{2V}\)
Height (h): \(\dfrac{V}{\sqrt{\dfrac{2V}{\sqrt[3]{2V}}} \cdot \sqrt[3]{2V}}\)

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Chapter 19

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Chapter 19

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Chapter 19

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Chapter 19

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Chapter 19

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