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anonymous
 5 years ago
If 1200 cm squared of material is available to make a box with a square base and an open top, find the largest possible volume of the box.
thank you
anonymous
 5 years ago
If 1200 cm squared of material is available to make a box with a square base and an open top, find the largest possible volume of the box. thank you

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radar
 5 years ago
Best ResponseYou've already chosen the best response.0The box will be formed by cutting in each side at the corners for a distance x and folding up the sides to form the box. The depth of the box will be x, the length and width will be 12002x. Units are cm. Volume V=x(12002x)(12002x) V=x)14400004800x+4x^2)

radar
 5 years ago
Best ResponseYou've already chosen the best response.0\[V=4x ^{3}4800x ^{2}+1440000\]

radar
 5 years ago
Best ResponseYou've already chosen the best response.0Differentiate and set to for max min

radar
 5 years ago
Best ResponseYou've already chosen the best response.0Solve for x the depth, the sides would be 12002x. Now if the material is 1200 sq cm and not a piece that is 1200 x1200 then use sides of 1200^sqrt.

radar
 5 years ago
Best ResponseYou've already chosen the best response.0The way I read it, was a piece of material 1200 by 1200

radar
 5 years ago
Best ResponseYou've already chosen the best response.0I see where I made a mistake in the multiplying failing to multiplying byx

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0thank you thank you! In this question, I'm given the surface area > 1200 = w^2 + 4 ( h x w )

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I apologize if I made the question confusing =(

radar
 5 years ago
Best ResponseYou've already chosen the best response.0O.K. I'm sorry. does the problem say you have a square piece of material that is 1200 cm sq?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Yes that is correct. I'm sorry for the confusion

radar
 5 years ago
Best ResponseYou've already chosen the best response.0Or is the completed box to have 1200 sq cm of surface area

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Hm... let me read again. I'm sorrry!!!

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Hm... let me read again. I'm sorrry!!!

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0if \[1200 cm ^{2 }\] of material is available to make a box with a square base and an open top, find the largest possible volume of the box

radar
 5 years ago
Best ResponseYou've already chosen the best response.0I am sorry, but I have to go pick up my car. If the problem is not solved when I get back tonight I will make furthert attempts to help. Thanks for clarify. I think I know what you are to do.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Thank you so much for you help sir!

radar
 5 years ago
Best ResponseYou've already chosen the best response.0I'm back. if you have 1200 cm^2 of material then you have a square whose sides are equal to the square root of 1200 or 34.64 cm. The box will be formed by cutting in each side at the corners for a distance x and folding up the sides to form the box. The depth of the box will be x, the length and width will be 34.642x. Units are cm.

radar
 5 years ago
Best ResponseYou've already chosen the best response.0Volume V=x(34.642x)(34.642x) V=(x)(1200138.56x+4x^2) V=1200x138.5x^2+4x^3

radar
 5 years ago
Best ResponseYou've already chosen the best response.0\[V=4x ^{3}138.5x ^{2}+1200x\]

radar
 5 years ago
Best ResponseYou've already chosen the best response.0Now differentiate and set to zero

radar
 5 years ago
Best ResponseYou've already chosen the best response.0Now you can use quadratic equation and solve for x which represents the depth and the sides would be 34.642x. Good luck
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