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

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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
-
should be


------correct surface area formula
-

(removed solution steps which followed)

Answer by ikleyn(52775)   (Show Source): You can put this solution on YOUR website!
.
The solution by "josgarithmetic" is WRONG.
Below find the correct solution.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

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 = 

-

   = 
= 
= 
-






, width

-

Length, 3w


Answer. Length = 30, width = 10, height = 15 inches.



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