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yashar806

  • 2 years ago

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.

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  1. tkhunny
    • 2 years ago
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    Can you describe the total surface area?

  2. yashar806
    • 2 years ago
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    im not sure

  3. tkhunny
    • 2 years ago
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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.

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

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

  6. yashar806
    • 2 years ago
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    am I right?

  7. tkhunny
    • 2 years ago
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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.

  8. yashar806
    • 2 years ago
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    I dont know how to find the surface area

  9. tkhunny
    • 2 years ago
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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.

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

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

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

  13. tkhunny
    • 2 years ago
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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?

  14. yashar806
    • 2 years ago
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    take the derivative

  15. tkhunny
    • 2 years ago
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    That's it. What do you get?

  16. yashar806
    • 2 years ago
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    2x -16/x^2

  17. tkhunny
    • 2 years ago
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    Perfect. Next?

  18. yashar806
    • 2 years ago
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    find the domain ?>

  19. yashar806
    • 2 years ago
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    0 to infinity ?

  20. yashar806
    • 2 years ago
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    then make it equal to 0

  21. yashar806
    • 2 years ago
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    i got x=2

  22. tkhunny
    • 2 years ago
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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).

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

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

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

  26. yashar806
    • 2 years ago
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    thank you

  27. tkhunny
    • 2 years ago
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    You did well. Excellent work!

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