SOLUTION: CALCULUS(MAXIMA AND MINIMA):A RECTANGULAR BOX HAVING A SQUARE BASE AND OPEN AT THE TOP IS TO HAVE A CAPACITY OF 16,823 CC.FIND THE HEIGHT OF THE TOP OF THE BOX TO USE THE LEAST AMO
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Question 1045809: CALCULUS(MAXIMA AND MINIMA):A RECTANGULAR BOX HAVING A SQUARE BASE AND OPEN AT THE TOP IS TO HAVE A CAPACITY OF 16,823 CC.FIND THE HEIGHT OF THE TOP OF THE BOX TO USE THE LEAST AMOUNT OF MATERIAL
Found 2 solutions by Alan3354, solver91311:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Stop using all CAPS.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Let 
be the measure of the side of the base and let 
be the height.
The volume of the box is 
, so 
The total surface area of a such a box is 
, but substitute for s from above:
\ = \frac{16823}{h}\ +\ 4h\sqrt{\frac{16823}{h}})
Find 
, set it equal to zero, and solve.
John
My calculator said it, I believe it, that settles it
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