anonymous
  • anonymous
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
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
radar
  • radar
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 1200-2x. Units are cm. Volume V=x(1200-2x)(1200-2x) V=x)1440000-4800x+4x^2)
radar
  • radar
\[V=4x ^{3}-4800x ^{2}+1440000\]
radar
  • radar
Differentiate and set to for max min

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

radar
  • radar
\[12x ^{2}-9600x=0\]
radar
  • radar
Solve for x the depth, the sides would be 1200-2x. Now if the material is 1200 sq cm and not a piece that is 1200 x1200 then use sides of 1200^sqrt.
radar
  • radar
The way I read it, was a piece of material 1200 by 1200
radar
  • radar
I see where I made a mistake in the multiplying failing to multiplying byx
anonymous
  • anonymous
thank you thank you! In this question, I'm given the surface area --> 1200 = w^2 + 4 ( h x w )
anonymous
  • anonymous
I apologize if I made the question confusing =(
radar
  • radar
O.K. I'm sorry. does the problem say you have a square piece of material that is 1200 cm sq?
anonymous
  • anonymous
Yes that is correct. I'm sorry for the confusion
radar
  • radar
Or is the completed box to have 1200 sq cm of surface area
anonymous
  • anonymous
Hm... let me read again. I'm sorrry!!!
anonymous
  • anonymous
Hm... let me read again. I'm sorrry!!!
anonymous
  • anonymous
if \[1200 cm ^{2 }\] 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
  • radar
I 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
  • anonymous
Thank you so much for you help sir!
radar
  • radar
I'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 34.64-2x. Units are cm.
radar
  • radar
Volume V=x(34.64-2x)(34.64-2x) V=(x)(1200-138.56x+4x^2) V=1200x-138.5x^2+4x^3
radar
  • radar
\[V=4x ^{3}-138.5x ^{2}+1200x\]
radar
  • radar
Now differentiate and set to zero
radar
  • radar
\[12x ^{2}-277x+1200=0\]
radar
  • radar
Now you can use quadratic equation and solve for x which represents the depth and the sides would be 34.64-2x. Good luck

Looking for something else?

Not the answer you are looking for? Search for more explanations.