SOLUTION: A box manufacturer is to produce a closed box of volume 4500 cubic inches, where the base is a rectangle having length three times its width. What are the dimensions of the box con
Question 1078617: A box manufacturer is to produce a closed box of volume 4500 cubic inches, where the base is a rectangle having length three times its width. What are the dimensions of the box constructed with the least amount of material?
To achieve a minimum surface area of ______________square inches, the box should be __________inches wide, _________inches long and _____________inches high. Found 2 solutions by josgarithmetic, ikleyn:Answer by josgarithmetic(39616) (Show Source): You can put this solution on YOUR website! Bottom or top dimensions,
length 3w, width w
h, for height
Given volume 4500,
Total surface area
Substitute for h.
total surface area: ------MISTAKEN STEP
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should be ------correct surface area formula
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Bottom or top dimensions,
length 3w, width w
h, for height
Given volume 4500,
(1)
Total surface area
S = = (2)
From (1), express h = and substitute it into (2). You will get
S =
-
=
=
=
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, width
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Length, 3w