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The folding box problem

Published online by Cambridge University Press:  22 September 2016

Nick Lord
Nick Lord*
Affiliation:
Tonbridge School, Tonbridge, Kent TN9 1JP
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Extract

A standard introductory calculus problem is to calculate the size of small squares that have to be removed from (say) a unit square of metal so that the resulting net folds into a tray of maximum volume. With notation as in the figure, this requires that be maximised which occurs when x = 2/3 giving a maximum volume of 2/27. (Surprisingly, this conclusion may also be reached without using calculus via the inequality of arithmetic and geometric means:

with equality if and only if or x = 2/3.)

Type
Research Article
Information
The Mathematical Gazette , Volume 74 , Issue 470 , December 1990 , pp. 361 - 365
Copyright
Copyright © Mathematical Association 1990 

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