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yashar806

an open top box with a square base has volume V=4m^3. Find the dimensions of the box so that it uses the least amount of material.

  • one year ago
  • one year ago

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  1. tkhunny
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    Can you describe the total surface area?

    • one year ago
  2. yashar806
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    im not sure

    • one year ago
  3. tkhunny
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    What is the measure of one side of the square base? If it is not given in the problemn statement, just name it something so we can talk about it.

    • one year ago
  4. yashar806
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    v= x^2 *y

    • one year ago
  5. yashar806
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    which will be y= 4/x^2

    • one year ago
  6. yashar806
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    am I right?

    • one year ago
  7. tkhunny
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    Well, it's okay, but I personally find it a little unsatisfactory for one reason. You did not tell us what you were doing. had you done this first, i woudl ahve been delighted. x = measurement of the side of the base y = measurement of the height of the box. You have discussed the volume. Now you need to discuss the surface area. Remember that it does not have a lid.

    • one year ago
  8. yashar806
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    I dont know how to find the surface area

    • one year ago
  9. tkhunny
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    Yes, you do. First, do we know WHY we need to talk about the surface area? Read the problem statement again and give me a clue.

    • one year ago
  10. yashar806
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    A= 2xy+2xy+2x^2 ?

    • one year ago
  11. yashar806
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    A=x^2+2xy+2xy

    • one year ago
  12. yashar806
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    A=X^2 + 16/x ?

    • one year ago
  13. tkhunny
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    There you go again, just blurting out equations without describing what you are doing. :-) So, who was right about you knowing how to find the Surface Area? Good work! What's next?

    • one year ago
  14. yashar806
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    take the derivative

    • one year ago
  15. tkhunny
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    That's it. What do you get?

    • one year ago
  16. yashar806
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    2x -16/x^2

    • one year ago
  17. tkhunny
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    Perfect. Next?

    • one year ago
  18. yashar806
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    find the domain ?>

    • one year ago
  19. yashar806
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    0 to infinity ?

    • one year ago
  20. yashar806
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    then make it equal to 0

    • one year ago
  21. yashar806
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    i got x=2

    • one year ago
  22. tkhunny
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    ?? I suppose. It's a REAL box, so x > 0. Infinity is probably not good. \(yx^{2} = 4\). It will be a very flat box if x > 5 or so. :et's just keep that in mind and find where that derivative is zero (0).

    • one year ago
  23. tkhunny
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    Yes, x = 2 is the only Real Solution.

    • one year ago
  24. tkhunny
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    Now, and finally, answer the original question. At this point, most folks have forgotten what the question was!

    • one year ago
  25. yashar806
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    box measures 2m*2m height of he box is 1m

    • one year ago
  26. yashar806
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    thank you

    • one year ago
  27. tkhunny
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    You did well. Excellent work!

    • one year ago
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