SOLUTION: An open square based container is to be made with a volume of 144 cm cubed. Calculate the exact dimension of the box if the surface area of the box is to be minimum.
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Question 990661: An open square based container is to be made with a volume of 144 cm cubed. Calculate the exact dimension of the box if the surface area of the box is to be minimum.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Let 
represent the measure of the side of the square bottom of the box. Let 
represent the height of the box.
The volume of the box is 
, so solving for , we get 
The surface area of an open box is the area of the 4 sides, 
plus the area of the bottom, 
So, the surface area as a function of the height of the box is:
\ =\ 48\sqrt{x}\ +\ \frac{144}{x})
Set the derivative equal to zero and solve for , then use .
John
My calculator said it, I believe it, that settles it
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