The Box Problem
Calculus
Level
3
A rectangular box, open at the top, is to have a volume of . What is the minimum value of its outside surface area in ?
The answer is 108.
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1 solution
This question can be solved by AM-GM Inequality
Since it is open box, TOTAL SURFACE AREA = lb + 2bh + 2lh
( lb+ 2bh + 2lh)/3≥∛((lb)(2bh)(2lh))
(lb+ 2bh + 2lh)/3≥∛(〖(2lbh)〗^2 )
Since lbh= 〖108 m〗^3
lb+2bh+2lh≥108 Q.E.D