a rectangular box of given volume is to be "a" times long as it is wide. find the dimension for which it has the least total surface area ?

L= aw
Total surface area= 2LW + 2Lh + 2Wh
= 2aw^2 + 2awh + 2wh

But volume= lwh= 2aw^2 h or h= V/2aw^2

Total Surface area= = 2aw^2 + 2awV/2aw^2 + 2wV/2aw^2

Take the derivative of surface area/with respect to w, solve.

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