A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

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

  • This Question is Closed
  1. radar
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    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)

  2. radar
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[V=4x ^{3}-4800x ^{2}+1440000\]

  3. radar
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Differentiate and set to for max min

  4. radar
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[12x ^{2}-9600x=0\]

  5. radar
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    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.

  6. radar
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    The way I read it, was a piece of material 1200 by 1200

  7. radar
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I see where I made a mistake in the multiplying failing to multiplying byx

  8. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    thank you thank you! In this question, I'm given the surface area --> 1200 = w^2 + 4 ( h x w )

  9. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I apologize if I made the question confusing =(

  10. radar
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    O.K. I'm sorry. does the problem say you have a square piece of material that is 1200 cm sq?

  11. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Yes that is correct. I'm sorry for the confusion

  12. radar
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Or is the completed box to have 1200 sq cm of surface area

  13. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Hm... let me read again. I'm sorrry!!!

  14. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Hm... let me read again. I'm sorrry!!!

  15. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    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

  16. radar
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    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.

  17. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Thank you so much for you help sir!

  18. radar
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    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.

  19. radar
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Volume V=x(34.64-2x)(34.64-2x) V=(x)(1200-138.56x+4x^2) V=1200x-138.5x^2+4x^3

  20. radar
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[V=4x ^{3}-138.5x ^{2}+1200x\]

  21. radar
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Now differentiate and set to zero

  22. radar
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[12x ^{2}-277x+1200=0\]

  23. radar
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Now you can use quadratic equation and solve for x which represents the depth and the sides would be 34.64-2x. Good luck

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

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.