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

Algebra ->  Test -> 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      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
Stop using all CAPS.

Answer by solver91311(24713) About Me  (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:



Find , set it equal to zero, and solve.

John

My calculator said it, I believe it, that settles it